Atkin-Lehner |
3- 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
1221a |
Isogeny class |
Conductor |
1221 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
112 |
Modular degree for the optimal curve |
Δ |
-32967 = -1 · 34 · 11 · 37 |
Discriminant |
Eigenvalues |
1 3- 2 -4 11+ -6 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,5,-7] |
[a1,a2,a3,a4,a6] |
Generators |
[13:41:1] |
Generators of the group modulo torsion |
j |
18191447/32967 |
j-invariant |
L |
3.565623445966 |
L(r)(E,1)/r! |
Ω |
1.9337022528036 |
Real period |
R |
1.8439361286342 |
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 |
19536y1 78144r1 3663e1 30525d1 |
Quadratic twists by: -4 8 -3 5 |