Atkin-Lehner |
3+ 5+ 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
34515a |
Isogeny class |
Conductor |
34515 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-4362089398875 = -1 · 33 · 53 · 135 · 592 |
Discriminant |
Eigenvalues |
-2 3+ 5+ -1 -5 13- -3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-16773,842128] |
[a1,a2,a3,a4,a6] |
Generators |
[142:1150:1] [-92:1267:1] |
Generators of the group modulo torsion |
j |
-19328234626732032/161558866625 |
j-invariant |
L |
4.1717073831667 |
L(r)(E,1)/r! |
Ω |
0.78068633632942 |
Real period |
R |
0.26718204155995 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999947 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34515b1 |
Quadratic twists by: -3 |