Atkin-Lehner |
2- 3+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
12936n |
Isogeny class |
Conductor |
12936 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
11740429008 = 24 · 34 · 77 · 11 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 11+ 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-101887,-12483848] |
[a1,a2,a3,a4,a6] |
Generators |
[7041:590155:1] |
Generators of the group modulo torsion |
j |
62140690757632/6237 |
j-invariant |
L |
4.5634407732481 |
L(r)(E,1)/r! |
Ω |
0.26722033761485 |
Real period |
R |
8.5387227895532 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25872w1 103488eb1 38808bg1 1848j1 |
Quadratic twists by: -4 8 -3 -7 |