Atkin-Lehner |
2+ 7- 17+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
78302a |
Isogeny class |
Conductor |
78302 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-8769968702096 = -1 · 24 · 79 · 172 · 47 |
Discriminant |
Eigenvalues |
2+ 1 -3 7- 5 2 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,4580,78250] |
[a1,a2,a3,a4,a6] |
Generators |
[53:-713:1] |
Generators of the group modulo torsion |
j |
263374721/217328 |
j-invariant |
L |
4.0684250117484 |
L(r)(E,1)/r! |
Ω |
0.47376864608062 |
Real period |
R |
1.0734208155068 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000613 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78302b1 |
Quadratic twists by: -7 |