Atkin-Lehner |
2- 3- 13- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
83304u |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
58368 |
Modular degree for the optimal curve |
Δ |
-5829947136 = -1 · 28 · 39 · 13 · 89 |
Discriminant |
Eigenvalues |
2- 3- -3 1 -5 13- 2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-399,4786] |
[a1,a2,a3,a4,a6] |
Generators |
[5:54:1] [-15:86:1] |
Generators of the group modulo torsion |
j |
-37642192/31239 |
j-invariant |
L |
9.065072754197 |
L(r)(E,1)/r! |
Ω |
1.2353824282831 |
Real period |
R |
0.45861672803634 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000008 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27768e1 |
Quadratic twists by: -3 |