Atkin-Lehner |
2- 3+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
12768s |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
429183552 = 26 · 3 · 76 · 19 |
Discriminant |
Eigenvalues |
2- 3+ -4 7- -6 0 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-190,-104] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:28:1] [-4:24:1] |
Generators of the group modulo torsion |
j |
11914842304/6705993 |
j-invariant |
L |
4.6679658268861 |
L(r)(E,1)/r! |
Ω |
1.3834399528392 |
Real period |
R |
1.1247243552342 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999984 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12768y1 25536dj2 38304z1 89376cs1 |
Quadratic twists by: -4 8 -3 -7 |