Atkin-Lehner |
2+ 3+ 5- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970p |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
8870400 |
Modular degree for the optimal curve |
Δ |
-9.740082885628E+21 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -5 11- 1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-28007872,57237247456] |
[a1,a2,a3,a4,a6] |
Generators |
[2167:80929:1] |
Generators of the group modulo torsion |
j |
-11335027914992789161/45438205500000 |
j-invariant |
L |
2.9368270885292 |
L(r)(E,1)/r! |
Ω |
0.12979789116636 |
Real period |
R |
1.8855128426843 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999998498 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970cd1 |
Quadratic twists by: -11 |