Atkin-Lehner |
5+ 31- 53- |
Signs for the Atkin-Lehner involutions |
Class |
8215b |
Isogeny class |
Conductor |
8215 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
12864 |
Modular degree for the optimal curve |
Δ |
-89419248125 = -1 · 54 · 312 · 533 |
Discriminant |
Eigenvalues |
-1 -1 5+ -2 4 3 7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-17331,871078] |
[a1,a2,a3,a4,a6] |
Generators |
[26:649:1] |
Generators of the group modulo torsion |
j |
-575699888159848369/89419248125 |
j-invariant |
L |
1.8083862865766 |
L(r)(E,1)/r! |
Ω |
1.0382378231784 |
Real period |
R |
0.14514868737239 |
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 |
73935k1 41075a1 |
Quadratic twists by: -3 5 |