Atkin-Lehner |
7- 29- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
8323d |
Isogeny class |
Conductor |
8323 |
Conductor |
∏ cp |
5 |
Product of Tamagawa factors cp |
deg |
17760 |
Modular degree for the optimal curve |
Δ |
-33592302163 = -1 · 75 · 29 · 413 |
Discriminant |
Eigenvalues |
2 2 -2 7- 4 -5 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-8814,-315701] |
[a1,a2,a3,a4,a6] |
Generators |
[100302:2110805:216] |
Generators of the group modulo torsion |
j |
-75734214083817472/33592302163 |
j-invariant |
L |
10.195656979676 |
L(r)(E,1)/r! |
Ω |
0.24635457771978 |
Real period |
R |
8.2772214537647 |
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 |
74907h1 58261o1 |
Quadratic twists by: -3 -7 |