Atkin-Lehner |
2+ 3- 5- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970bd |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
2128896 |
Modular degree for the optimal curve |
Δ |
-5.3443527493158E+19 |
Discriminant |
Eigenvalues |
2+ 3- 5- 1 11- -1 5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1567558,-833411944] |
[a1,a2,a3,a4,a6] |
Generators |
[3640:-206008:1] |
Generators of the group modulo torsion |
j |
-1987250838862201/249318000000 |
j-invariant |
L |
6.8774010613675 |
L(r)(E,1)/r! |
Ω |
0.066992618934483 |
Real period |
R |
0.71291032288569 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994325 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970ct1 |
Quadratic twists by: -11 |