Atkin-Lehner |
2+ 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
19942c |
Isogeny class |
Conductor |
19942 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
-291616492544 = -1 · 210 · 136 · 59 |
Discriminant |
Eigenvalues |
2+ -1 -1 -3 -2 13+ -2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-4228,107216] |
[a1,a2,a3,a4,a6] |
Generators |
[8:268:1] [31:69:1] |
Generators of the group modulo torsion |
j |
-1732323601/60416 |
j-invariant |
L |
4.1034913155682 |
L(r)(E,1)/r! |
Ω |
0.96752238787857 |
Real period |
R |
1.0603091377987 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
118b1 |
Quadratic twists by: 13 |