Atkin-Lehner |
2+ 3+ 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360a |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
2658994601040 = 24 · 34 · 5 · 177 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 0 -2 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-663351,-207731070] |
[a1,a2,a3,a4,a6] |
Generators |
[-115757197190597974:901438623044392:246362173188769] |
Generators of the group modulo torsion |
j |
83587439220736/6885 |
j-invariant |
L |
4.1696506071144 |
L(r)(E,1)/r! |
Ω |
0.16728756326955 |
Real period |
R |
24.925048379021 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985906 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34680p1 4080o1 |
Quadratic twists by: -4 17 |