Atkin-Lehner |
2+ 7+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
39872c |
Isogeny class |
Conductor |
39872 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
-670128704 = -1 · 26 · 76 · 89 |
Discriminant |
Eigenvalues |
2+ -3 3 7+ -6 4 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5851,-172268] |
[a1,a2,a3,a4,a6] |
Generators |
[158490:1697507:1000] |
Generators of the group modulo torsion |
j |
-346125847768128/10470761 |
j-invariant |
L |
3.8199063693444 |
L(r)(E,1)/r! |
Ω |
0.27293626630556 |
Real period |
R |
6.997799195115 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000008 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39872o1 19936g1 |
Quadratic twists by: -4 8 |