Atkin-Lehner |
2+ 3+ 17- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
12648a |
Isogeny class |
Conductor |
12648 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
6336 |
Modular degree for the optimal curve |
Δ |
-3626029824 = -1 · 28 · 3 · 173 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -2 -3 -3 17- -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-561,6069] |
[a1,a2,a3,a4,a6] |
Generators |
[-25:62:1] [3145:-10642:125] |
Generators of the group modulo torsion |
j |
-76409304064/14164179 |
j-invariant |
L |
5.1428970712671 |
L(r)(E,1)/r! |
Ω |
1.3472355597152 |
Real period |
R |
0.1590570976428 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25296g1 101184q1 37944i1 |
Quadratic twists by: -4 8 -3 |