Atkin-Lehner |
3+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
22743g |
Isogeny class |
Conductor |
22743 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
862109794498113 = 39 · 72 · 197 |
Discriminant |
Eigenvalues |
1 3+ 0 7- -2 6 8 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-185802,-30747673] |
[a1,a2,a3,a4,a6] |
Generators |
[20586459850:560977078383:20796875] |
Generators of the group modulo torsion |
j |
766060875/931 |
j-invariant |
L |
6.6404631165763 |
L(r)(E,1)/r! |
Ω |
0.22996860007626 |
Real period |
R |
14.43776044724 |
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 |
22743i1 1197b1 |
Quadratic twists by: -3 -19 |