Atkin-Lehner |
2- 3- 31- 43- |
Signs for the Atkin-Lehner involutions |
Class |
47988i |
Isogeny class |
Conductor |
47988 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
37632 |
Modular degree for the optimal curve |
Δ |
-34003720944 = -1 · 24 · 313 · 31 · 43 |
Discriminant |
Eigenvalues |
2- 3- 2 4 -3 2 -5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-309,-9115] |
[a1,a2,a3,a4,a6] |
Generators |
[115:1215:1] |
Generators of the group modulo torsion |
j |
-279738112/2915271 |
j-invariant |
L |
8.1844236894105 |
L(r)(E,1)/r! |
Ω |
0.49430505792581 |
Real period |
R |
1.3797862200941 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15996c1 |
Quadratic twists by: -3 |