Atkin-Lehner |
2+ 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
9968c |
Isogeny class |
Conductor |
9968 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-35372524544 = -1 · 210 · 72 · 893 |
Discriminant |
Eigenvalues |
2+ -3 -1 7- -2 -4 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,197,8986] |
[a1,a2,a3,a4,a6] |
Generators |
[115:1246:1] |
Generators of the group modulo torsion |
j |
825700284/34543481 |
j-invariant |
L |
2.1619098852322 |
L(r)(E,1)/r! |
Ω |
0.87870061225289 |
Real period |
R |
0.20502905607494 |
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 |
4984d1 39872bm1 89712d1 69776d1 |
Quadratic twists by: -4 8 -3 -7 |