Atkin-Lehner |
2- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
51376p |
Isogeny class |
Conductor |
51376 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-23477598976 = -1 · 28 · 136 · 19 |
Discriminant |
Eigenvalues |
2- -2 1 -3 5 13+ -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3605,82447] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:338:1] [31:38:1] |
Generators of the group modulo torsion |
j |
-4194304/19 |
j-invariant |
L |
7.2288232946105 |
L(r)(E,1)/r! |
Ω |
1.2065872907489 |
Real period |
R |
1.4977829101203 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12844d1 304f1 |
Quadratic twists by: -4 13 |