Atkin-Lehner |
2+ 7+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
129584b |
Isogeny class |
Conductor |
129584 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-754697216 = -1 · 210 · 72 · 132 · 89 |
Discriminant |
Eigenvalues |
2+ -1 1 7+ 0 13+ -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-40,-1312] |
[a1,a2,a3,a4,a6] |
Generators |
[13:14:1] [14:26:1] |
Generators of the group modulo torsion |
j |
-7086244/737009 |
j-invariant |
L |
10.450131816802 |
L(r)(E,1)/r! |
Ω |
0.70792853226018 |
Real period |
R |
1.845195407878 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002052 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64792c1 |
Quadratic twists by: -4 |