Atkin-Lehner |
3- 11+ 29+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
89001d |
Isogeny class |
Conductor |
89001 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
494592 |
Modular degree for the optimal curve |
Δ |
11920222880480673 = 313 · 11 · 294 · 312 |
Discriminant |
Eigenvalues |
-1 3- 2 -2 11+ 0 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-82724,7522206] |
[a1,a2,a3,a4,a6] |
Generators |
[-232:3882:1] [574:10887:8] |
Generators of the group modulo torsion |
j |
85878774786616057/16351471715337 |
j-invariant |
L |
7.7112651692841 |
L(r)(E,1)/r! |
Ω |
0.381481066794 |
Real period |
R |
5.0535045123911 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999994075 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
29667a1 |
Quadratic twists by: -3 |