Atkin-Lehner |
2+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712a |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1078272 |
Modular degree for the optimal curve |
Δ |
-1572370900499316736 = -1 · 214 · 76 · 138 |
Discriminant |
Eigenvalues |
2+ 0 1 7+ 2 13+ -3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1573052,761778992] |
[a1,a2,a3,a4,a6] |
Generators |
[676:2704:1] |
Generators of the group modulo torsion |
j |
-32209663824/117649 |
j-invariant |
L |
6.2127128696172 |
L(r)(E,1)/r! |
Ω |
0.26862090156868 |
Real period |
R |
1.9273484286068 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999998817 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75712ck1 4732a1 75712x1 |
Quadratic twists by: -4 8 13 |