Atkin-Lehner |
3+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
8349a |
Isogeny class |
Conductor |
8349 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
19200 |
Modular degree for the optimal curve |
Δ |
-291126583975887 = -1 · 310 · 118 · 23 |
Discriminant |
Eigenvalues |
1 3+ 0 2 11- -2 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2785,821704] |
[a1,a2,a3,a4,a6] |
Generators |
[-4442060:6832582:42875] |
Generators of the group modulo torsion |
j |
-1349232625/164333367 |
j-invariant |
L |
4.4240953037236 |
L(r)(E,1)/r! |
Ω |
0.44884685110817 |
Real period |
R |
9.8565809090581 |
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 |
25047e1 759a1 |
Quadratic twists by: -3 -11 |