Atkin-Lehner |
2+ 3+ 5- 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
88110d |
Isogeny class |
Conductor |
88110 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
1259712 |
Modular degree for the optimal curve |
Δ |
-19269657000000000 = -1 · 29 · 39 · 59 · 11 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 0 11+ 5 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1334409,593681165] |
[a1,a2,a3,a4,a6] |
Generators |
[661:-668:1] |
Generators of the group modulo torsion |
j |
-13350560217951989187/979000000000 |
j-invariant |
L |
5.3472237392732 |
L(r)(E,1)/r! |
Ω |
0.36727332754496 |
Real period |
R |
0.80884715323813 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002361 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
88110bt1 |
Quadratic twists by: -3 |