Atkin-Lehner |
7- 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12397q |
Isogeny class |
Conductor |
12397 |
Conductor |
∏ cp |
14 |
Product of Tamagawa factors cp |
deg |
23296 |
Modular degree for the optimal curve |
Δ |
153734292019 = 73 · 117 · 23 |
Discriminant |
Eigenvalues |
-1 -3 -3 7- 11- -1 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1434,9342] |
[a1,a2,a3,a4,a6] |
Generators |
[758:-7159:8] [2:79:1] |
Generators of the group modulo torsion |
j |
950152003191/448204933 |
j-invariant |
L |
2.2226505857706 |
L(r)(E,1)/r! |
Ω |
0.91629250222621 |
Real period |
R |
0.17326427504396 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111573q1 12397p1 |
Quadratic twists by: -3 -7 |