Atkin-Lehner |
2- 3- 31+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
68076a |
Isogeny class |
Conductor |
68076 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
118272 |
Modular degree for the optimal curve |
Δ |
-108981779184 = -1 · 24 · 310 · 31 · 612 |
Discriminant |
Eigenvalues |
2- 3- 3 1 -6 0 0 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-19821,1074197] |
[a1,a2,a3,a4,a6] |
Generators |
[43:549:1] |
Generators of the group modulo torsion |
j |
-73833403019008/9343431 |
j-invariant |
L |
7.9989221716742 |
L(r)(E,1)/r! |
Ω |
1.0170925924364 |
Real period |
R |
0.65537479346156 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991037 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22692b1 |
Quadratic twists by: -3 |