Atkin-Lehner |
2+ 3+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
117216c |
Isogeny class |
Conductor |
117216 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
811008 |
Modular degree for the optimal curve |
Δ |
3142362028272192 = 26 · 39 · 113 · 374 |
Discriminant |
Eigenvalues |
2+ 3+ -4 2 11+ 2 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-60237,-5010660] |
[a1,a2,a3,a4,a6] |
Generators |
[-25626:147439:216] |
Generators of the group modulo torsion |
j |
19188562851648/2494508291 |
j-invariant |
L |
5.3911684042063 |
L(r)(E,1)/r! |
Ω |
0.30735515073318 |
Real period |
R |
8.7702587570929 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994358 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117216y1 117216x1 |
Quadratic twists by: -4 -3 |