Atkin-Lehner |
2- 5+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82810bw |
Isogeny class |
Conductor |
82810 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
9953280 |
Modular degree for the optimal curve |
Δ |
-17814882176000 = -1 · 210 · 53 · 77 · 132 |
Discriminant |
Eigenvalues |
2- -1 5+ 7- 0 13+ 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-487515701,-4143356637477] |
[a1,a2,a3,a4,a6] |
Generators |
[39494384536473:1787274591348484:1493271207] |
Generators of the group modulo torsion |
j |
-644487634439863642624729/896000 |
j-invariant |
L |
6.8299502516435 |
L(r)(E,1)/r! |
Ω |
0.016064692138435 |
Real period |
R |
21.257644381814 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11830u1 82810bf1 |
Quadratic twists by: -7 13 |