Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312y |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
248832 |
Modular degree for the optimal curve |
Δ |
-29802891313152 = -1 · 222 · 39 · 192 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -3 -2 -7 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,5599,205473] |
[a1,a2,a3,a4,a6] |
j |
205083359/314928 |
j-invariant |
L |
0.90027906651267 |
L(r)(E,1)/r! |
Ω |
0.45013953908203 |
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 |
69312du1 2166e1 69312bj1 |
Quadratic twists by: -4 8 -19 |