Atkin-Lehner |
3+ 5+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
61005c |
Isogeny class |
Conductor |
61005 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
35885886225 = 3 · 52 · 78 · 83 |
Discriminant |
Eigenvalues |
1 3+ 5+ 7- -2 -4 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-12373,-534848] |
[a1,a2,a3,a4,a6] |
Generators |
[-522:281:8] [1182:6955:8] |
Generators of the group modulo torsion |
j |
1780800847561/305025 |
j-invariant |
L |
9.2873958661393 |
L(r)(E,1)/r! |
Ω |
0.45266893864612 |
Real period |
R |
10.258485919009 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999901 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8715k1 |
Quadratic twists by: -7 |