Atkin-Lehner |
2+ 7- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
33418m |
Isogeny class |
Conductor |
33418 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
659568 |
Modular degree for the optimal curve |
Δ |
-6464198236360933376 = -1 · 226 · 710 · 11 · 31 |
Discriminant |
Eigenvalues |
2+ 0 -3 7- 11- 1 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,465344,5787648] |
[a1,a2,a3,a4,a6] |
Generators |
[1066624:1101049024:1] |
Generators of the group modulo torsion |
j |
39451647395223/22884122624 |
j-invariant |
L |
2.6785211171251 |
L(r)(E,1)/r! |
Ω |
0.14285681087483 |
Real period |
R |
9.3748456959181 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33418e1 |
Quadratic twists by: -7 |