Atkin-Lehner |
2+ 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264n |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
72559927596259584 = 28 · 320 · 133 · 37 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 0 13+ -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-270111,52456030] |
[a1,a2,a3,a4,a6] |
Generators |
[462:5126:1] |
Generators of the group modulo torsion |
j |
11678391514890448/388802767041 |
j-invariant |
L |
4.1695873923324 |
L(r)(E,1)/r! |
Ω |
0.34349403101761 |
Real period |
R |
6.0693738709729 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999997471 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34632n1 23088i1 |
Quadratic twists by: -4 -3 |