Atkin-Lehner |
2+ 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
69776a |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-1261439550350336 = -1 · 210 · 712 · 89 |
Discriminant |
Eigenvalues |
2+ 1 1 7- 0 -4 -5 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-139960,20179396] |
[a1,a2,a3,a4,a6] |
Generators |
[240:686:1] [1080:33614:1] |
Generators of the group modulo torsion |
j |
-2516809936036/10470761 |
j-invariant |
L |
12.37370853511 |
L(r)(E,1)/r! |
Ω |
0.48672861686858 |
Real period |
R |
3.1777740475564 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34888a1 9968a1 |
Quadratic twists by: -4 -7 |