Atkin-Lehner |
2+ 3- 7- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384l |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
12799518482688 = 28 · 3 · 710 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- -4 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-6092,60192] |
[a1,a2,a3,a4,a6] |
Generators |
[20484:2931768:1] |
Generators of the group modulo torsion |
j |
830321872/424977 |
j-invariant |
L |
9.1333846292871 |
L(r)(E,1)/r! |
Ω |
0.62644414487384 |
Real period |
R |
7.2898635128941 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000135 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9912e1 |
Quadratic twists by: -7 |