Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312v |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-131806751145984 = -1 · 214 · 32 · 197 |
Discriminant |
Eigenvalues |
2+ 3+ 3 1 5 -6 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,3851,-545939] |
[a1,a2,a3,a4,a6] |
j |
8192/171 |
j-invariant |
L |
2.2717944200822 |
L(r)(E,1)/r! |
Ω |
0.28397430177892 |
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 |
69312ds1 4332d1 3648m1 |
Quadratic twists by: -4 8 -19 |