Atkin-Lehner |
2+ 5+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82810j |
Isogeny class |
Conductor |
82810 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1419264 |
Modular degree for the optimal curve |
Δ |
-4655799404721920000 = -1 · 211 · 54 · 73 · 139 |
Discriminant |
Eigenvalues |
2+ -1 5+ 7- 1 13+ -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-688678,242954132] |
[a1,a2,a3,a4,a6] |
Generators |
[-589:21382:1] [629:7375:1] |
Generators of the group modulo torsion |
j |
-21818208730807/2812160000 |
j-invariant |
L |
6.2503461625187 |
L(r)(E,1)/r! |
Ω |
0.23688102788393 |
Real period |
R |
1.6491258867586 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997965 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82810bd1 6370ba1 |
Quadratic twists by: -7 13 |