Atkin-Lehner |
3- 5- 7+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
12075t |
Isogeny class |
Conductor |
12075 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
52992 |
Modular degree for the optimal curve |
Δ |
236723626463625 = 33 · 53 · 78 · 233 |
Discriminant |
Eigenvalues |
-1 3- 5- 7+ 0 4 -8 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-30218,-1883973] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:274:1] |
Generators of the group modulo torsion |
j |
24412471425434357/1893789011709 |
j-invariant |
L |
3.4585754837926 |
L(r)(E,1)/r! |
Ω |
0.36388299755384 |
Real period |
R |
3.1682120416384 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
36225cc1 12075p1 84525ba1 |
Quadratic twists by: -3 5 -7 |