Atkin-Lehner |
2+ 5+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
31850u |
Isogeny class |
Conductor |
31850 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
304128 |
Modular degree for the optimal curve |
Δ |
-271351808000000000 = -1 · 224 · 59 · 72 · 132 |
Discriminant |
Eigenvalues |
2+ 1 5+ 7- 0 13- 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-227526,48695448] |
[a1,a2,a3,a4,a6] |
Generators |
[1461:52517:1] |
Generators of the group modulo torsion |
j |
-1701366814932001/354418688000 |
j-invariant |
L |
4.5186514698955 |
L(r)(E,1)/r! |
Ω |
0.29638079255703 |
Real period |
R |
1.9057626132376 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6370n1 31850b1 |
Quadratic twists by: 5 -7 |