Atkin-Lehner |
2+ 3+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
2112c |
Isogeny class |
Conductor |
2112 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
-101376 = -1 · 210 · 32 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 11+ 2 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,11,-11] |
[a1,a2,a3,a4,a6] |
Generators |
[4:9:1] |
Generators of the group modulo torsion |
j |
131072/99 |
j-invariant |
L |
2.2685201891135 |
L(r)(E,1)/r! |
Ω |
1.8783083603505 |
Real period |
R |
1.2077464153384 |
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 |
2112bc1 132a1 6336ba1 52800cd1 |
Quadratic twists by: -4 8 -3 5 |