Atkin-Lehner |
3+ 5- 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
48165k |
Isogeny class |
Conductor |
48165 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-653429268375 = -1 · 3 · 53 · 136 · 192 |
Discriminant |
Eigenvalues |
-1 3+ 5- 2 2 13+ 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,250,-38758] |
[a1,a2,a3,a4,a6] |
Generators |
[32:41:1] |
Generators of the group modulo torsion |
j |
357911/135375 |
j-invariant |
L |
3.813811717255 |
L(r)(E,1)/r! |
Ω |
0.42656504327992 |
Real period |
R |
2.9802502395504 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999964 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
285b1 |
Quadratic twists by: 13 |