Atkin-Lehner |
2- 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
9968f |
Isogeny class |
Conductor |
9968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-42888237056 = -1 · 212 · 76 · 89 |
Discriminant |
Eigenvalues |
2- 1 1 7+ 4 2 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,440,-9164] |
[a1,a2,a3,a4,a6] |
Generators |
[195:2744:1] |
Generators of the group modulo torsion |
j |
2294744759/10470761 |
j-invariant |
L |
5.5809748306266 |
L(r)(E,1)/r! |
Ω |
0.57612581980242 |
Real period |
R |
2.4217690992137 |
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 |
623a1 39872bb1 89712q1 69776o1 |
Quadratic twists by: -4 8 -3 -7 |