Atkin-Lehner |
2- 3+ 31- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69936m |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1203840 |
Modular degree for the optimal curve |
Δ |
554272356399316992 = 231 · 311 · 31 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 -2 -6 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1438248,663406704] |
[a1,a2,a3,a4,a6] |
Generators |
[-1276:20480:1] |
Generators of the group modulo torsion |
j |
80327713009607043625/135320399511552 |
j-invariant |
L |
3.4098817972294 |
L(r)(E,1)/r! |
Ω |
0.29168842033709 |
Real period |
R |
2.9225378520106 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985809 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8742e1 |
Quadratic twists by: -4 |