Atkin-Lehner |
2- 3+ 5- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970cd |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
806400 |
Modular degree for the optimal curve |
Δ |
-5498022865500000 = -1 · 25 · 314 · 56 · 112 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5- 5 11- -1 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-231470,-43108405] |
[a1,a2,a3,a4,a6] |
Generators |
[4773:325663:1] |
Generators of the group modulo torsion |
j |
-11335027914992789161/45438205500000 |
j-invariant |
L |
11.127794614462 |
L(r)(E,1)/r! |
Ω |
0.10880320267024 |
Real period |
R |
1.7045752241457 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997288 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970p1 |
Quadratic twists by: -11 |