Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bt |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
Δ |
2.1697500146647E+19 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 0 2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1837249,-932562529] |
[a1,a2,a3,a4,a6] |
Generators |
[-271873:1760520:343] |
Generators of the group modulo torsion |
j |
111223479026/3518667 |
j-invariant |
L |
7.0382664488099 |
L(r)(E,1)/r! |
Ω |
0.12992685151981 |
Real period |
R |
9.0284986855567 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997434 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312cq4 8664i3 3648i3 |
Quadratic twists by: -4 8 -19 |