Atkin-Lehner |
2+ 7- 13- 67- |
Signs for the Atkin-Lehner involutions |
Class |
12194d |
Isogeny class |
Conductor |
12194 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
7776 |
Modular degree for the optimal curve |
Δ |
-12194 = -1 · 2 · 7 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ 1 3 7- 0 13- 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-5842,171358] |
[a1,a2,a3,a4,a6] |
j |
-22044563397858457/12194 |
j-invariant |
L |
2.4529775959711 |
L(r)(E,1)/r! |
Ω |
2.4529775959711 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
97552f1 109746w1 85358g1 |
Quadratic twists by: -4 -3 -7 |