Atkin-Lehner |
2- 7- 11+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
8162j |
Isogeny class |
Conductor |
8162 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
26112 |
Modular degree for the optimal curve |
Δ |
-8917556209408 = -1 · 28 · 7 · 116 · 532 |
Discriminant |
Eigenvalues |
2- 2 -2 7- 11+ -4 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-6689,252127] |
[a1,a2,a3,a4,a6] |
Generators |
[-25:648:1] |
Generators of the group modulo torsion |
j |
-33098732111216017/8917556209408 |
j-invariant |
L |
7.7023375191781 |
L(r)(E,1)/r! |
Ω |
0.69532874465277 |
Real period |
R |
1.384657541201 |
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 |
65296p1 73458r1 57134s1 89782c1 |
Quadratic twists by: -4 -3 -7 -11 |