Atkin-Lehner |
2+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
40768s |
Isogeny class |
Conductor |
40768 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-1403264565248 = -1 · 217 · 77 · 13 |
Discriminant |
Eigenvalues |
2+ -1 0 7- -3 13+ -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1633,62945] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:272:1] [89:784:1] |
Generators of the group modulo torsion |
j |
-31250/91 |
j-invariant |
L |
7.441678973697 |
L(r)(E,1)/r! |
Ω |
0.75160062251722 |
Real period |
R |
0.61881925310056 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40768co1 5096c1 5824l1 |
Quadratic twists by: -4 8 -7 |