Atkin-Lehner |
3+ 23- 31- |
Signs for the Atkin-Lehner involutions |
Class |
66309h |
Isogeny class |
Conductor |
66309 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2419200 |
Modular degree for the optimal curve |
Δ |
-147771048255990219 = -1 · 35 · 23 · 319 |
Discriminant |
Eigenvalues |
-2 3+ 3 4 2 0 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-2493154,1516150542] |
[a1,a2,a3,a4,a6] |
Generators |
[317730:282843:343] |
Generators of the group modulo torsion |
j |
-1931083438845952/166501899 |
j-invariant |
L |
4.0617470571377 |
L(r)(E,1)/r! |
Ω |
0.31104391967303 |
Real period |
R |
3.2646089503997 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001501 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2139e1 |
Quadratic twists by: -31 |