Atkin-Lehner |
3- 11+ 19- 37- |
Signs for the Atkin-Lehner involutions |
Class |
69597d |
Isogeny class |
Conductor |
69597 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
Δ |
2786032565613 = 36 · 11 · 193 · 373 |
Discriminant |
Eigenvalues |
0 3- 0 -4 11+ -4 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-6330,176427] |
[a1,a2,a3,a4,a6] |
Generators |
[-73:499:1] [-55:598:1] |
Generators of the group modulo torsion |
j |
38477541376000/3821718197 |
j-invariant |
L |
7.2884498506588 |
L(r)(E,1)/r! |
Ω |
0.78341346116466 |
Real period |
R |
4.6517262033359 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999955 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
7733d2 |
Quadratic twists by: -3 |