Atkin-Lehner |
2+ 3- 31+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
82584c |
Isogeny class |
Conductor |
82584 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192000 |
Modular degree for the optimal curve |
Δ |
-111198828948912 = -1 · 24 · 38 · 315 · 37 |
Discriminant |
Eigenvalues |
2+ 3- 0 1 4 1 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6330,543121] |
[a1,a2,a3,a4,a6] |
Generators |
[-76:765:1] |
Generators of the group modulo torsion |
j |
-2404846336000/9533507283 |
j-invariant |
L |
7.4513502905706 |
L(r)(E,1)/r! |
Ω |
0.51752383260734 |
Real period |
R |
3.5995203600531 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001932 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27528g1 |
Quadratic twists by: -3 |