Atkin-Lehner |
2+ 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264i |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-8976678285442608 = -1 · 24 · 315 · 134 · 372 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 -4 13+ 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,40290,3330187] |
[a1,a2,a3,a4,a6] |
Generators |
[993259:21827646:4913] |
Generators of the group modulo torsion |
j |
620108955392000/769605477147 |
j-invariant |
L |
5.7804196909124 |
L(r)(E,1)/r! |
Ω |
0.27573193514801 |
Real period |
R |
10.481955395284 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000621 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34632l1 23088h1 |
Quadratic twists by: -4 -3 |