Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192l |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
11925323061331968 = 211 · 38 · 316 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 4 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3324099,-2332694882] |
[a1,a2,a3,a4,a6] |
Generators |
[-7061891411380848216720994:-225589917683950984746945:6716656801613054502136] |
Generators of the group modulo torsion |
j |
3065617154/9 |
j-invariant |
L |
8.2604190496714 |
L(r)(E,1)/r! |
Ω |
0.11181012776937 |
Real period |
R |
36.939493830388 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998161 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23064m6 72a5 |
Quadratic twists by: -3 -31 |