Atkin-Lehner |
3- 23- 59- |
Signs for the Atkin-Lehner involutions |
Class |
12213b |
Isogeny class |
Conductor |
12213 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3360 |
Modular degree for the optimal curve |
Δ |
-22752819 = -1 · 36 · 232 · 59 |
Discriminant |
Eigenvalues |
1 3- 3 1 0 4 2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-468,4023] |
[a1,a2,a3,a4,a6] |
j |
-15568817473/31211 |
j-invariant |
L |
4.286235490548 |
L(r)(E,1)/r! |
Ω |
2.143117745274 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1357a1 |
Quadratic twists by: -3 |