Atkin-Lehner |
2+ 3- 31+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
8742f |
Isogeny class |
Conductor |
8742 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1248 |
Modular degree for the optimal curve |
Δ |
-26226 = -1 · 2 · 32 · 31 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -3 -4 -1 0 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,0,-8] |
[a1,a2,a3,a4,a6] |
Generators |
[2:0:1] |
Generators of the group modulo torsion |
j |
12167/26226 |
j-invariant |
L |
2.4911003810949 |
L(r)(E,1)/r! |
Ω |
1.7464501201273 |
Real period |
R |
0.71318967326517 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69936n1 26226s1 |
Quadratic twists by: -4 -3 |