Atkin-Lehner |
2- 3+ 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12078n |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
9600 |
Modular degree for the optimal curve |
Δ |
-26414586 = -1 · 2 · 39 · 11 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 1 -2 11+ 1 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-5132,142777] |
[a1,a2,a3,a4,a6] |
j |
-759299343867/1342 |
j-invariant |
L |
3.6185983954259 |
L(r)(E,1)/r! |
Ω |
1.8092991977129 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96624z1 12078c1 |
Quadratic twists by: -4 -3 |