Atkin-Lehner |
37- 43- |
Signs for the Atkin-Lehner involutions |
Class |
68413b |
Isogeny class |
Conductor |
68413 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1374912 |
Modular degree for the optimal curve |
Δ |
-688049285741538067 = -1 · 372 · 439 |
Discriminant |
Eigenvalues |
2 0 2 4 -5 1 3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-131279,-43907741] |
[a1,a2,a3,a4,a6] |
Generators |
[14154108934358794006:15252309737472074951657:12189231526744] |
Generators of the group modulo torsion |
j |
-39582093312/108845083 |
j-invariant |
L |
15.848435758453 |
L(r)(E,1)/r! |
Ω |
0.11635160919619 |
Real period |
R |
34.052893354767 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1591a1 |
Quadratic twists by: -43 |