Atkin-Lehner |
2- 3+ 5- 23- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
40710z |
Isogeny class |
Conductor |
40710 |
Conductor |
∏ cp |
608 |
Product of Tamagawa factors cp |
deg |
894976 |
Modular degree for the optimal curve |
Δ |
-517753036800000000 = -1 · 219 · 34 · 58 · 232 · 59 |
Discriminant |
Eigenvalues |
2- 3+ 5- -1 -5 -5 -7 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-673800,215400585] |
[a1,a2,a3,a4,a6] |
Generators |
[613:5453:1] [453:-2067:1] |
Generators of the group modulo torsion |
j |
-33831150905261634307201/517753036800000000 |
j-invariant |
L |
11.166204807957 |
L(r)(E,1)/r! |
Ω |
0.29407826775132 |
Real period |
R |
0.06245095421219 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122130j1 |
Quadratic twists by: -3 |