Atkin-Lehner |
2- 3+ 11- 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
31746z |
Isogeny class |
Conductor |
31746 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
253968 = 24 · 3 · 11 · 13 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 2 0 11- 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-332,-2467] |
[a1,a2,a3,a4,a6] |
Generators |
[10568:-3425:512] |
Generators of the group modulo torsion |
j |
4047806261953/253968 |
j-invariant |
L |
8.5127515730894 |
L(r)(E,1)/r! |
Ω |
1.1184326990655 |
Real period |
R |
7.6113221476822 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
95238k1 |
Quadratic twists by: -3 |