Timeline for BSD conjecture for X_0(17)
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Sep 7, 2013 at 13:29 | vote | accept | Carl | ||
| Sep 7, 2013 at 13:29 | vote | accept | Carl | ||
| Sep 7, 2013 at 13:29 | |||||
| Aug 17, 2013 at 12:38 | answer | added | Joe Silverman | timeline score: 16 | |
| Aug 16, 2013 at 17:52 | vote | accept | Carl | ||
| Sep 7, 2013 at 13:29 | |||||
| Aug 16, 2013 at 16:20 | answer | added | Tim Dokchitser | timeline score: 28 | |
| Aug 16, 2013 at 12:51 | history | edited | user9072 |
edited tags
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| Aug 16, 2013 at 12:16 | comment | added | Carl | I see, so L(E,1)/Ω∞ = (1/(4^2))*1 = 1/16, but it should be 1/8. | |
| Aug 16, 2013 at 12:14 | comment | added | Tim Dokchitser | For elliptic curves with positive discriminant, $E({\mathbb R})$ has two connected components, and the BSD period is twice the real period. If you divide by that, you get $1/16$. In Magma you can use ConjecturalRegulator(E) to get the conjectural order of sha times the regulator - this is 1 in this case. (It takes the correct BSD period, and divides by that and the product of Tamagawa numbers and multiplies by torsion^2) | |
| Aug 16, 2013 at 12:11 | comment | added | joro | According to sage Sha(E)=1 | |
| Aug 16, 2013 at 11:57 | comment | added | Carl | According to the BSD formula, why did I get 1/16? There must be something wrong. | |
| Aug 16, 2013 at 11:54 | comment | added | joro | btw, here: wstein.org/books/bsd/bsd/node27.html they use the Regulator and Omega too. I get correct result with the code in the link. | |
| Aug 16, 2013 at 11:50 | comment | added | joro | e0.tamagawa_number(17) = 1, not sure if this is what you are asking. | |
| Aug 16, 2013 at 11:42 | review | First posts | |||
| Aug 16, 2013 at 12:09 | |||||
| Aug 16, 2013 at 11:40 | comment | added | Carl | Thanks. Could you please calculate the Tamagawa factor to look if it is 1? | |
| Aug 16, 2013 at 11:38 | comment | added | joro | For lseries you need to import eulerprod.py. The code is: sage: e0=EllipticCurve(QQ,[1, -1, 1, -1, 0]);pl=e0.period_lattice();l0=LSeries(e0);l0(1) / pl.real_period() 0.125000000000000 | |
| Aug 16, 2013 at 11:35 | comment | added | Carl | What is going on with the BSD? I am deeply puzzled. | |
| Aug 16, 2013 at 11:30 | comment | added | joro | I get 1/8 in sage too using the equivalent of your commands. | |
| Aug 16, 2013 at 11:29 | comment | added | Carl | By the way, how could I compute Sha(E) and the Tamagawa factor c_p(E) by Magma? | |
| Aug 16, 2013 at 11:22 | history | asked | Carl | CC BY-SA 3.0 |