Atkin-Lehner |
2+ 3+ 23+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
32568a |
Isogeny class |
Conductor |
32568 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-31616589192192 = -1 · 210 · 36 · 233 · 592 |
Discriminant |
Eigenvalues |
2+ 3+ 2 4 -2 2 -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-192,-270468] |
[a1,a2,a3,a4,a6] |
j |
-768400132/30875575383 |
j-invariant |
L |
2.4045507480516 |
L(r)(E,1)/r! |
Ω |
0.3005688435056 |
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 |
65136f1 97704m1 |
Quadratic twists by: -4 -3 |