Atkin-Lehner |
2+ 3- 5+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
51480k |
Isogeny class |
Conductor |
51480 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-5909757426144000 = -1 · 28 · 36 · 53 · 117 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11- 13+ 1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-50268,5700692] |
[a1,a2,a3,a4,a6] |
Generators |
[214:-2178:1] |
Generators of the group modulo torsion |
j |
-75271580947456/31666652875 |
j-invariant |
L |
4.6480953270072 |
L(r)(E,1)/r! |
Ω |
0.3990630182441 |
Real period |
R |
0.20799146619278 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102960v1 5720g1 |
Quadratic twists by: -4 -3 |