Atkin-Lehner |
2- 3+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12696m |
Isogeny class |
Conductor |
12696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1152 |
Modular degree for the optimal curve |
Δ |
-3656448 = -1 · 28 · 33 · 232 |
Discriminant |
Eigenvalues |
2- 3+ -2 1 -2 1 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,31,-75] |
[a1,a2,a3,a4,a6] |
Generators |
[3:6:1] |
Generators of the group modulo torsion |
j |
23552/27 |
j-invariant |
L |
3.3636543277528 |
L(r)(E,1)/r! |
Ω |
1.3421434522582 |
Real period |
R |
1.2530904658862 |
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 |
25392o1 101568y1 38088c1 12696k1 |
Quadratic twists by: -4 8 -3 -23 |