Atkin-Lehner |
2+ 7+ 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
12194a |
Isogeny class |
Conductor |
12194 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1184 |
Modular degree for the optimal curve |
Δ |
-97552 = -1 · 24 · 7 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ 2 2 7+ 2 13+ 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,11,-3] |
[a1,a2,a3,a4,a6] |
Generators |
[6:15:1] |
Generators of the group modulo torsion |
j |
127263527/97552 |
j-invariant |
L |
5.3553386949173 |
L(r)(E,1)/r! |
Ω |
1.8810571511506 |
Real period |
R |
1.4234917561228 |
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 |
97552i1 109746o1 85358j1 |
Quadratic twists by: -4 -3 -7 |