Atkin-Lehner |
2- 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712bh |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-46629126144 = -1 · 220 · 36 · 61 |
Discriminant |
Eigenvalues |
2- 3- 3 1 -3 1 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-289,-10657] |
[a1,a2,a3,a4,a6] |
Generators |
[71:576:1] |
Generators of the group modulo torsion |
j |
-10218313/177876 |
j-invariant |
L |
6.6673806238247 |
L(r)(E,1)/r! |
Ω |
0.48749198759972 |
Real period |
R |
0.56987095800394 |
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 |
11712e1 2928k1 35136cc1 |
Quadratic twists by: -4 8 -3 |