Atkin-Lehner |
2+ 3+ 5+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
69600h |
Isogeny class |
Conductor |
69600 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
189225000000 = 26 · 32 · 58 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -4 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7258,239512] |
[a1,a2,a3,a4,a6] |
Generators |
[-69:638:1] [-2:504:1] |
Generators of the group modulo torsion |
j |
42289683904/189225 |
j-invariant |
L |
8.9922710236859 |
L(r)(E,1)/r! |
Ω |
1.0139550895257 |
Real period |
R |
4.434255085142 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000018 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
69600br1 13920bg1 |
Quadratic twists by: -4 5 |