Atkin-Lehner |
2+ 3+ 7+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
69384b |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
161280 |
Modular degree for the optimal curve |
Δ |
-35704779236784 = -1 · 24 · 38 · 78 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ 3 7+ 4 6 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1601,-286964] |
[a1,a2,a3,a4,a6] |
j |
4917248/387099 |
j-invariant |
L |
3.7228988367758 |
L(r)(E,1)/r! |
Ω |
0.31024157065303 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69384n1 |
Quadratic twists by: -7 |