Atkin-Lehner |
2+ 3- 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360bs |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
261120 |
Modular degree for the optimal curve |
Δ |
-142305451796400 = -1 · 24 · 3 · 52 · 179 |
Discriminant |
Eigenvalues |
2+ 3- 5- 4 0 -2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3275,-579552] |
[a1,a2,a3,a4,a6] |
Generators |
[11636357498079989024149284:-107163163835549271873934770:84330494379961913916377] |
Generators of the group modulo torsion |
j |
-2048/75 |
j-invariant |
L |
10.258890381858 |
L(r)(E,1)/r! |
Ω |
0.25344379071655 |
Real period |
R |
40.477970883226 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000681 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34680n1 69360i1 |
Quadratic twists by: -4 17 |