Atkin-Lehner |
2+ 3- 5+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
31680y |
Isogeny class |
Conductor |
31680 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-162972972518400 = -1 · 210 · 314 · 52 · 113 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11- 0 8 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,11112,-417112] |
[a1,a2,a3,a4,a6] |
Generators |
[49:495:1] |
Generators of the group modulo torsion |
j |
203269830656/218317275 |
j-invariant |
L |
5.1384118288804 |
L(r)(E,1)/r! |
Ω |
0.31076157356475 |
Real period |
R |
1.3779084100654 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31680ck1 3960q1 10560j1 |
Quadratic twists by: -4 8 -3 |