Atkin-Lehner |
2- 3- 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68544eb |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
2457845172038592 = 26 · 318 · 73 · 172 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 4 -2 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1191711,-500725384] |
[a1,a2,a3,a4,a6] |
j |
4011705594213827392/52680152007 |
j-invariant |
L |
1.1559715396199 |
L(r)(E,1)/r! |
Ω |
0.14449644414271 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544ex1 34272m4 22848bt1 |
Quadratic twists by: -4 8 -3 |