Atkin-Lehner |
2+ 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712h |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-35979264 = -1 · 216 · 32 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -1 3 3 5 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1,-289] |
[a1,a2,a3,a4,a6] |
j |
-4/549 |
j-invariant |
L |
3.7671798057246 |
L(r)(E,1)/r! |
Ω |
0.94179495143116 |
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 |
11712q1 1464e1 35136k1 |
Quadratic twists by: -4 8 -3 |