I read that Frey's curve is a semi-stable elliptic curve. What doe this mean ? I can find two dimensional representations of $y^2 = x^3 + ax + b$ in Wikipedia. What does $y^2 = x(x-a)(x+b)$ look like if $a$ and $b$ are solutions to $FLT$ ?
How can I transform the elliptic curve $E/\mathbb{C}$ of the form $$y^2=4(x-e_1)(x-e_2)(x-e_3)$$ with $e_1&gt;e_2&gt;e_3\in\mathbb{R}$ roots of $E$ into a Weierstrass-Form $y^2=x^3+ax+b$?
Proof that every metric space is normal From yesterday, openweather extention on the top panel does not show the weather. Its shows "Please wait Loading".  I tried to find the solution. There was a post of creating account on openweather website and use API id. I found that it is a subscription base plan. There was a free plan which allows 60 calls free for weather data.  I thought that the extention is open source. And may be I deleted any package that is required to work the extention so I reinstall the OS. But there is no difference of doing that.    What could possibly go wrong any guidance? The other day I was looking at Stack Overflow on my Android phone. All is made very nice and all, but I could not find the Review button/link. Is it being implemented, did I miss it, or it is not available? How are "Suggested Tags" chosen? After you've typed in a question, you get suggested tags that appear that look like this:        It appears that you need a minimum amount of characters ():     you must have entered a title (any length) and a minimum body length of 220 characters.   But other than that, how are the tags chosen? Is it:   A match of the title/body with other questions (taking the tags from those questions) A match of the title/body with tag excerpts (taking tags with overlap) A match of the title/body with tag wikis (taking tags with overlap) All of the Above None of the Above Other (please explain)   Some additional info from :  The suggested tags seem to only pop up on meta.so (they do not work on regular Stack Overflow, or on other SE sites).  While we're on the topic, why isn't this feature implemented network-wide? Rearranging display order of attribute table fields using QGIS? Using QGIS 2.10.1, I open an attribute table.  How do I rearrange the field display order?  For example, a table's default display order (from left to right) is State, County, City.  But I would like to see them displayed as City, State, County.  I'm not interested in rearranging the table's internal structure, rather just the table's display. Determining Min - Max within zip code (statistics by area)? I'm new to ArcGIS Desktop. I have created a layer representing zip codes and overlayed it with a layer containing some data points. I want to find the min and max value of the data points in each zip code. Currently, I am manually checking the values if all the data points in each zip code but this is becoming very time-consuming and cumbersome.   Is there a faster way to do this? Show that the square of any prime number is the Factof of some integer How to enable fast user switching when Login Options are disabled? hyperref: how to format text in a forms text-field I would like to pre-format the text in a form text-field, e.g. make it bold, italic or use a specific font. The following code generates a simple text-field:  \documentclass{scrreprt} \usepackage{hyperref} \begin{document} \textbf{The Text Field} \begin{Form} \TextField[]{\ } \end{Form} \end{document}   Is it possible to pre-format the text in the text-field? The hyperref package manual (10/2011) speaks of an optional parameter format and the use of JavaScript to format the field. Can this be used to format the text in the field? And if yes, how is it done? (I am not proficient in JavaScript) I am a photography newbie and have only a 18 - 135mm canon kit lens at my disposal. I wanted to take macro shots but can't really afford a macro lens right now. One very optimistic goal of mine is to capture a single snow flake this winter.   Is there any cheap(er) way to take macro shots? Also, any specific advice from anyone one how to go about photographing a single snow flake. Salesforce, Oracle and the Seven Dwarfs Over my time as a Salesforce developer, I've written some code which on occasion managed to surface Oracle plsql exceptions and curiously the error text contains the name of one of Disney's .  I've teased out Doc, Grumpy, Happy, Bashful and Sneezy. I'm sure the other two are not far away.   What is the underlying "thing" on the database platform that is named after a Dwarf? Why were these named after Dwarves?      java.sql.SQLException: ORA-30006: resource busy; acquire with WAIT   timeout expiredORA-06512: at "DOC.CAPEX", line 2200ORA-06512: at line   1: SQLException while executing plsql statement: {call   cApex.update_sysmodstamp(?)}([       java.sql.SQLException: ORA-30006: resource busy; acquire with WAIT   timeout expiredORA-06512: at "GRUMPY.CAPEX", line 2563ORA-06512: at   line 1: SQLException while executing plsql statement: {call   cApex.update_sysmodstamp(?)}([       java.sql.SQLException: ORA-30006: resource busy; acquire with WAIT   timeout expiredORA-06512: at "HAPPY.CAPEX", line 2715ORA-06512: at   line 1: SQLException while executing plsql statement: {call   cApex.update_sysmodstamp(?)}([       java.sql.SQLException: ORA-30006: resource busy; acquire with WAIT   timeout expiredORA-06512: at "BASHFUL.CAPEX", line 2715ORA-06512: at   line 1: SQLException while executing plsql statement: {call   cApex.update_sysmodstamp(?)}([       java.sql.SQLException: ORA-30006: resource busy; acquire with WAIT   timeout expiredORA-06512: at "SNEEZY.CAPEX", line 2718ORA-06512: at   line 1: SQLException while executing plsql statement: {call   cApex.invalidate_agc(?,?)}([      Error: ORA-20000: ORA-06512: at "SNEEZY.SIMPORTLOOKUP", line 850   ORA-06512: at "SNEEZY.SIMPORTLOOKUP", line 823 ORA-06512: at line 1 :   SQLException while executing plsql statement: {call   sImportLookup.get_by_ext_id_text(?,?,?,?,?,?,?)}([ How do I learn to become a good GM? I have played and tried to GM games since I was in elementary school, beginning with games like Shadowrun, Earthdawn, and Champions. Recently, I've gotten dack into gaming with a variety of other games (newer Shadowrun and Earthdawn, plus TOON! and Outbreak:Undead).  I've found examples of actual play and advice on how to actually GM a game in games to be lacking. I can only help but feel I am not alone as someone who isn't already a LITERAL dungeon MASTER.  I fully realize that there are an unlimited number of GM styles, personalities, etc. I do not think I am a very good GM though. No one else wants to be the GM, and few care enough to learn the complex rules that I often have to assist with and explain AS WE PLAY. Being left with the responsibility is quite overwhelming unless I create dynamic encounters or make it all up on the spot. I'm often left having no idea what to do.  Examples of Why I Think I Need Help  This question isn't about these examples so please don't dig into them in the answers - they're here to explain the basic things that leave me feeling like I don't know how to proceed as a GM.  I've read preparation is important, but last time I tried to make a story, the players immediately killed the primary character (a friendly person.) within about 2 minutes of starting the game. While I realize now that I let the dice take control over the story, it was rather difficult to continue a story that relied on this friendly character, with the players making enemies with the character's faction. It is still discouraging when my only other attempt at a prepared story ended with the players wanting to go in a complete opposite direction of where I planned. Both times, the hours of work I put into it were completely wasted, leaving me as ignorant as I always was before.  My group often wants to play Shadowrun, Earthdawn, or L5R- but I feel as though I am a horrible GM. The last time we played Shadowrun, I was bored out of my mind as we rolled hundreds of dice to do an obvious straight-forward "kick down the door" mission.   If I make security as I believe it should or as the forum threads describe their security or a few example missions I can scrounge up (examples of stories, not actual gameplay), my players literally feel completely hopeless as to how to achieve their mission without total failure.   One time when I was a teenager, I had players blow up at me saying "We have no idea what would work. You're telling us that our character's experience or the ally operative says that would get us killed, but what else can we do?" Since there are no examples of what players can do - I am left with the same feeling as the players. As an adult, I've had a similar occurrence where a player said to me, "I don't know what to do. I don't think we can even begin this mission." I had to make something up and just go with it, creating an NPC group (that fit in with the story) that goes in before the players to do something stupid so they don't have to. Mainly because I ALSO didn't know how to accomplish the mission, so I acted as the players would using my NPC group. Extremely boring and IMO a failed dungeon run.  I've had successful stories, but I've had more boring encounters than successful ones. Seeing as how roleplaying takes endless hours to complete a story, I do not see benefit in an activity that wastes more time than is enjoyable.  How Do You Learn To GM?  Where are the resources? Books, blogs, gameplay examples? Am I missing them? How did YOU learn to be a good GM? Or do you feel as bad at this as I do, even when it's a successful, fun encounter? overset text over equal sign in in an Align environment How do I create an Excel (.XLS and .XLSX) file in C# without installing Microsoft Office? How can I create an Excel spreadsheet with C# without requiring Excel to be installed on the machine that's running the code? I was recently reading some Lord of the Rings/Stargate SG-1 crossover fanfiction. It is a guilty pleasure, I admit :) In this story, it was suggested by Col. O'Neill to destroy the Ring using a nuclear device. Truth be told I stopped reading at this point, as it was getting to be a little much even for me.  Obviously, this is not canonical in either universe, but it made me wonder: When Elrond said that "only in the fires of Mt. Doom may it be unmade," was he speaking literally? Or was this merely the only known active volcano in Middle Earth? In other words, was whatever magic that protected the One Ring from damage location-based or did it just make it very resistant to destructive force, and Mt. Doom just happened to be hot enough to do this? I know there is (understandably) little information about such technicalities of how magic works in Middle Earth, but I'll accept any reasonable conjecture/consensus as an answer. How do I mount a hibernated NTFS partition? How to close aberrant tooltips in Windows So, here I am, trying to watch The Cleveland Show (TM).      And, as happens from time to time, some program or another has left a modal tooltip.  I don't know which program; how can I lose the tooltip, short of logoff/reboot?  Currently happening on Windows 10, but I have seen it on other versions. Split seeds.rb into multiple sections? How to prove that any idempotent matrix is diagonalizable? To what extent is WhatsApp's statement on secure messaging realistic?