Atkin-Lehner |
2+ 3+ 5+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970a |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
2703360 |
Modular degree for the optimal curve |
Δ |
9.5128951100513E+19 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 11+ -2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-2314248,-1272192192] |
[a1,a2,a3,a4,a6] |
Generators |
[13749:1595058:1] |
Generators of the group modulo torsion |
j |
581325709271579/40343961600 |
j-invariant |
L |
3.779978403289 |
L(r)(E,1)/r! |
Ω |
0.1229392602769 |
Real period |
R |
7.6866787610681 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994754 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68970bj1 |
Quadratic twists by: -11 |