Atkin-Lehner |
2+ 3+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
85176k |
Isogeny class |
Conductor |
85176 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
309969773568 = 210 · 39 · 7 · 133 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- -4 13- 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1755,9126] |
[a1,a2,a3,a4,a6] |
Generators |
[-174:1539:8] |
Generators of the group modulo torsion |
j |
13500/7 |
j-invariant |
L |
6.3609719900532 |
L(r)(E,1)/r! |
Ω |
0.85223775877946 |
Real period |
R |
3.7319233520146 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004933 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85176bp1 85176bl1 |
Quadratic twists by: -3 13 |