Atkin-Lehner |
2+ 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
7568g |
Isogeny class |
Conductor |
7568 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
1152 |
Modular degree for the optimal curve |
Δ |
915728 = 24 · 113 · 43 |
Discriminant |
Eigenvalues |
2+ -2 2 1 11- -6 -6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32,43] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:11:1] |
Generators of the group modulo torsion |
j |
233644288/57233 |
j-invariant |
L |
3.2853879640201 |
L(r)(E,1)/r! |
Ω |
2.6253680520623 |
Real period |
R |
0.41713363597906 |
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 |
3784b1 30272x1 68112i1 83248o1 |
Quadratic twists by: -4 8 -3 -11 |