Atkin-Lehner |
3- 19- 89- |
Signs for the Atkin-Lehner involutions |
Class |
15219g |
Isogeny class |
Conductor |
15219 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
96000 |
Modular degree for the optimal curve |
Δ |
-9486326911102731 = -1 · 316 · 195 · 89 |
Discriminant |
Eigenvalues |
1 3- 1 -4 -3 -3 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-113994,-15508989] |
[a1,a2,a3,a4,a6] |
Generators |
[786:19101:1] [1926:82143:1] |
Generators of the group modulo torsion |
j |
-224721335000834209/13012794116739 |
j-invariant |
L |
7.777323249337 |
L(r)(E,1)/r! |
Ω |
0.12947693922524 |
Real period |
R |
3.0033623345888 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999977 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5073g1 |
Quadratic twists by: -3 |