Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bm |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-9980928 = -1 · 210 · 33 · 192 |
Discriminant |
Eigenvalues |
2+ 3- 0 3 -2 1 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-253,1475] |
[a1,a2,a3,a4,a6] |
Generators |
[11:12:1] |
Generators of the group modulo torsion |
j |
-4864000/27 |
j-invariant |
L |
8.9677089397163 |
L(r)(E,1)/r! |
Ω |
2.3048389479483 |
Real period |
R |
0.64846967197612 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000573 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312cl1 8664h1 69312a1 |
Quadratic twists by: -4 8 -19 |