Atkin-Lehner |
2- 3+ 29- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
84912r |
Isogeny class |
Conductor |
84912 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
-118197504 = -1 · 28 · 32 · 292 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 3 1 3 5 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,116,172] |
[a1,a2,a3,a4,a6] |
Generators |
[49:348:1] |
Generators of the group modulo torsion |
j |
668510768/461709 |
j-invariant |
L |
8.3256645923007 |
L(r)(E,1)/r! |
Ω |
1.1784073261696 |
Real period |
R |
1.7662960011609 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000592 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21228b1 |
Quadratic twists by: -4 |