Atkin-Lehner |
5- 11+ 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
13585i |
Isogeny class |
Conductor |
13585 |
Conductor |
∏ cp |
70 |
Product of Tamagawa factors cp |
deg |
35840 |
Modular degree for the optimal curve |
Δ |
-66687703671875 = -1 · 57 · 112 · 135 · 19 |
Discriminant |
Eigenvalues |
-1 1 5- 3 11+ 13- 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-37765,-2855108] |
[a1,a2,a3,a4,a6] |
Generators |
[249:1663:1] |
Generators of the group modulo torsion |
j |
-5956524027302481361/66687703671875 |
j-invariant |
L |
4.0751617568819 |
L(r)(E,1)/r! |
Ω |
0.17112262659255 |
Real period |
R |
0.34020396768161 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122265r1 67925b1 |
Quadratic twists by: -3 5 |