Atkin-Lehner |
2+ 5+ 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
30680b |
Isogeny class |
Conductor |
30680 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
75264 |
Modular degree for the optimal curve |
Δ |
-427188320000000 = -1 · 211 · 57 · 13 · 593 |
Discriminant |
Eigenvalues |
2+ -1 5+ 0 -2 13- -2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-35256,-2723444] |
[a1,a2,a3,a4,a6] |
Generators |
[22575:634132:27] |
Generators of the group modulo torsion |
j |
-2366492816943218/208588046875 |
j-invariant |
L |
3.2919806369507 |
L(r)(E,1)/r! |
Ω |
0.1733332398268 |
Real period |
R |
6.3307354093195 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61360b1 |
Quadratic twists by: -4 |