Atkin-Lehner |
2+ 3+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
23712b |
Isogeny class |
Conductor |
23712 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5376 |
Modular degree for the optimal curve |
Δ |
-27316224 = -1 · 212 · 33 · 13 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -1 0 13+ 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-81,-351] |
[a1,a2,a3,a4,a6] |
j |
-14526784/6669 |
j-invariant |
L |
1.5553686846313 |
L(r)(E,1)/r! |
Ω |
0.77768434231559 |
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 |
23712p1 47424bp1 71136bc1 |
Quadratic twists by: -4 8 -3 |