Atkin-Lehner |
2- 29- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
68672bd |
Isogeny class |
Conductor |
68672 |
Conductor |
∏ cp |
14 |
Product of Tamagawa factors cp |
deg |
444416 |
Modular degree for the optimal curve |
Δ |
-41828052070105088 = -1 · 216 · 297 · 37 |
Discriminant |
Eigenvalues |
2- -1 0 -4 -3 0 -5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-24513,9958369] |
[a1,a2,a3,a4,a6] |
Generators |
[-69:3364:1] |
Generators of the group modulo torsion |
j |
-24857124866500/638245423433 |
j-invariant |
L |
1.5631711933602 |
L(r)(E,1)/r! |
Ω |
0.30297217312579 |
Real period |
R |
0.36853247654924 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999957425 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68672j1 17168c1 |
Quadratic twists by: -4 8 |