Atkin-Lehner |
3+ 7- 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
11193d |
Isogeny class |
Conductor |
11193 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
12384 |
Modular degree for the optimal curve |
Δ |
316230982431 = 3 · 76 · 13 · 413 |
Discriminant |
Eigenvalues |
1 3+ -1 7- 1 13- -1 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2963,-57126] |
[a1,a2,a3,a4,a6] |
Generators |
[-38:68:1] |
Generators of the group modulo torsion |
j |
2878376935864249/316230982431 |
j-invariant |
L |
4.309416453392 |
L(r)(E,1)/r! |
Ω |
0.65167830688751 |
Real period |
R |
1.1021328590723 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33579k1 78351n1 |
Quadratic twists by: -3 -7 |