Atkin-Lehner |
2- 3+ 11+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
31152o |
Isogeny class |
Conductor |
31152 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-498432 = -1 · 28 · 3 · 11 · 59 |
Discriminant |
Eigenvalues |
2- 3+ 2 -4 11+ 3 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,3,33] |
[a1,a2,a3,a4,a6] |
Generators |
[1:6:1] |
Generators of the group modulo torsion |
j |
8192/1947 |
j-invariant |
L |
4.3682295577932 |
L(r)(E,1)/r! |
Ω |
2.2766066357492 |
Real period |
R |
0.95937293013192 |
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 |
7788a1 124608dj1 93456bu1 |
Quadratic twists by: -4 8 -3 |