Atkin-Lehner |
11- 17- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
121363g |
Isogeny class |
Conductor |
121363 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
237312 |
Modular degree for the optimal curve |
Δ |
-20850490716011 = -1 · 114 · 176 · 59 |
Discriminant |
Eigenvalues |
0 1 -3 -1 11- -4 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-8147,-361025] |
[a1,a2,a3,a4,a6] |
Generators |
[263:3969:1] |
Generators of the group modulo torsion |
j |
-4085069283328/1424116571 |
j-invariant |
L |
1.6796069512643 |
L(r)(E,1)/r! |
Ω |
0.24691928322087 |
Real period |
R |
3.4011256571164 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999995979161 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
121363a1 |
Quadratic twists by: -11 |