Atkin-Lehner |
3- 7+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
67431i |
Isogeny class |
Conductor |
67431 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
51456 |
Modular degree for the optimal curve |
Δ |
-40922457849 = -1 · 34 · 72 · 134 · 192 |
Discriminant |
Eigenvalues |
-1 3- -1 7+ 0 13+ -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-426,10269] |
[a1,a2,a3,a4,a6] |
Generators |
[15:-93:1] [27:-150:1] |
Generators of the group modulo torsion |
j |
-299393809/1432809 |
j-invariant |
L |
7.5706013524826 |
L(r)(E,1)/r! |
Ω |
0.99517446420062 |
Real period |
R |
0.15848563963744 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000024 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67431r1 |
Quadratic twists by: 13 |