Atkin-Lehner |
2- 3+ 7- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
86688bf |
Isogeny class |
Conductor |
86688 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
821760 |
Modular degree for the optimal curve |
Δ |
10370544785911296 = 29 · 39 · 7 · 435 |
Discriminant |
Eigenvalues |
2- 3+ -1 7- -6 5 7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-355563,-81458946] |
[a1,a2,a3,a4,a6] |
Generators |
[-42295:41714:125] |
Generators of the group modulo torsion |
j |
493301168454744/1029059101 |
j-invariant |
L |
5.9280982225502 |
L(r)(E,1)/r! |
Ω |
0.19553515239293 |
Real period |
R |
7.5793254406864 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003761 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86688c1 86688e1 |
Quadratic twists by: -4 -3 |