Atkin-Lehner |
3+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
3393d |
Isogeny class |
Conductor |
3393 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
6720 |
Modular degree for the optimal curve |
Δ |
-211936643451 = -1 · 39 · 135 · 29 |
Discriminant |
Eigenvalues |
-2 3+ -3 0 -6 13- 1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-2889,63740] |
[a1,a2,a3,a4,a6] |
Generators |
[12:175:1] |
Generators of the group modulo torsion |
j |
-135479955456/10767497 |
j-invariant |
L |
1.2929791855322 |
L(r)(E,1)/r! |
Ω |
0.97975502482189 |
Real period |
R |
0.13196964065249 |
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 |
54288bc1 3393b1 84825e1 44109l1 |
Quadratic twists by: -4 -3 5 13 |