Atkin-Lehner |
2- 3+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68952s |
Isogeny class |
Conductor |
68952 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
2064384 |
Modular degree for the optimal curve |
Δ |
83103356829212928 = 28 · 34 · 138 · 173 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 2 13+ 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-22420948,-40855414172] |
[a1,a2,a3,a4,a6] |
Generators |
[38164:7395102:1] |
Generators of the group modulo torsion |
j |
1008754689437602000/67254057 |
j-invariant |
L |
4.8580808662547 |
L(r)(E,1)/r! |
Ω |
0.069380282194628 |
Real period |
R |
2.917544145023 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998503 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5304b1 |
Quadratic twists by: 13 |