Atkin-Lehner |
2- 3+ 5+ 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
57120be |
Isogeny class |
Conductor |
57120 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
1074043310760000 = 26 · 38 · 54 · 72 · 174 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ 0 2 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1365526,614636776] |
[a1,a2,a3,a4,a6] |
Generators |
[555:5236:1] |
Generators of the group modulo torsion |
j |
4399911864308960802496/16781926730625 |
j-invariant |
L |
4.4665053991164 |
L(r)(E,1)/r! |
Ω |
0.43087408799774 |
Real period |
R |
2.591537483749 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996132 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
57120ca1 114240jx2 |
Quadratic twists by: -4 8 |