Atkin-Lehner |
2- 3+ 7+ 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
82992bt |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1492992 |
Modular degree for the optimal curve |
Δ |
-1065205162240966656 = -1 · 216 · 312 · 73 · 13 · 193 |
Discriminant |
Eigenvalues |
2- 3+ -3 7+ 3 13- 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-689512,-225669776] |
[a1,a2,a3,a4,a6] |
Generators |
[518734094:15257869398:357911] |
Generators of the group modulo torsion |
j |
-8850949862460130153/260059854062736 |
j-invariant |
L |
4.0031678346854 |
L(r)(E,1)/r! |
Ω |
0.082695575461105 |
Real period |
R |
12.102122183979 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003663 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10374g1 |
Quadratic twists by: -4 |