Atkin-Lehner |
2- 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312de |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
8171520 |
Modular degree for the optimal curve |
Δ |
4.7359932951671E+22 |
Discriminant |
Eigenvalues |
2- 3- -2 -4 -2 4 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-22342049,-39283146273] |
[a1,a2,a3,a4,a6] |
Generators |
[6087:224256:1] |
Generators of the group modulo torsion |
j |
14580432307/559872 |
j-invariant |
L |
5.4729962663954 |
L(r)(E,1)/r! |
Ω |
0.069605673118715 |
Real period |
R |
5.6163281981952 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001318 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312f1 17328q1 69312ci1 |
Quadratic twists by: -4 8 -19 |