Atkin-Lehner |
2- 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
12936t |
Isogeny class |
Conductor |
12936 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
-250024176154368 = -1 · 28 · 34 · 77 · 114 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 11- -6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1356,760068] |
[a1,a2,a3,a4,a6] |
Generators |
[-64:638:1] [-42:792:1] |
Generators of the group modulo torsion |
j |
9148592/8301447 |
j-invariant |
L |
5.1806950683377 |
L(r)(E,1)/r! |
Ω |
0.43292934330202 |
Real period |
R |
1.4958258052064 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
25872q1 103488df1 38808v1 1848k1 |
Quadratic twists by: -4 8 -3 -7 |