Atkin-Lehner |
2+ 3- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
21312p |
Isogeny class |
Conductor |
21312 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
51200 |
Modular degree for the optimal curve |
Δ |
-859103428608 = -1 · 217 · 311 · 37 |
Discriminant |
Eigenvalues |
2+ 3- -4 -1 -3 5 -7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7212,239920] |
[a1,a2,a3,a4,a6] |
Generators |
[-90:400:1] [-28:648:1] |
Generators of the group modulo torsion |
j |
-434163602/8991 |
j-invariant |
L |
6.0618350992788 |
L(r)(E,1)/r! |
Ω |
0.8894126284198 |
Real period |
R |
0.42597179486654 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21312bv1 2664h1 7104h1 |
Quadratic twists by: -4 8 -3 |