Atkin-Lehner |
2+ 3+ 7+ 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12558c |
Isogeny class |
Conductor |
12558 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
41472 |
Modular degree for the optimal curve |
Δ |
6636680773632 = 224 · 33 · 72 · 13 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ -4 13- 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9606,-344556] |
[a1,a2,a3,a4,a6] |
Generators |
[-59:175:1] |
Generators of the group modulo torsion |
j |
98044243279969897/6636680773632 |
j-invariant |
L |
2.0015416857334 |
L(r)(E,1)/r! |
Ω |
0.48428691626309 |
Real period |
R |
4.1329666743382 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
100464ce1 37674s1 87906q1 |
Quadratic twists by: -4 -3 -7 |