Atkin-Lehner |
2- 3- 11+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
12078s |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
11648 |
Modular degree for the optimal curve |
Δ |
-2066207616 = -1 · 27 · 37 · 112 · 61 |
Discriminant |
Eigenvalues |
2- 3- -3 -4 11+ -6 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-554,5609] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:31:1] [-9:103:1] |
Generators of the group modulo torsion |
j |
-25750777177/2834304 |
j-invariant |
L |
7.2476981293471 |
L(r)(E,1)/r! |
Ω |
1.4308188367222 |
Real period |
R |
0.09045392579378 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96624bt1 4026d1 |
Quadratic twists by: -4 -3 |