Atkin-Lehner |
5- 7- 71- |
Signs for the Atkin-Lehner involutions |
Class |
86975bc |
Isogeny class |
Conductor |
86975 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1756160 |
Modular degree for the optimal curve |
Δ |
-397309634544921875 = -1 · 59 · 79 · 712 |
Discriminant |
Eigenvalues |
0 -3 5- 7- -5 -1 -7 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,171500,-13130469] |
[a1,a2,a3,a4,a6] |
Generators |
[441:-12177:1] [725:22187:1] |
Generators of the group modulo torsion |
j |
7077888/5041 |
j-invariant |
L |
4.7511989558637 |
L(r)(E,1)/r! |
Ω |
0.16888758829702 |
Real period |
R |
3.5165394655236 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999894 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86975ba1 86975z1 |
Quadratic twists by: 5 -7 |