Atkin-Lehner |
2- 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
8722o |
Isogeny class |
Conductor |
8722 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-42888237056 = -1 · 212 · 76 · 89 |
Discriminant |
Eigenvalues |
2- -1 -3 7- -6 -2 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,293,9897] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:56:1] [-1:98:1] |
Generators of the group modulo torsion |
j |
23639903/364544 |
j-invariant |
L |
5.9646981284502 |
L(r)(E,1)/r! |
Ω |
0.84807365827744 |
Real period |
R |
0.14652565037225 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69776y1 78498t1 178a1 |
Quadratic twists by: -4 -3 -7 |