Atkin-Lehner |
2- 5+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
30400bq |
Isogeny class |
Conductor |
30400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
-9728000000000000 = -1 · 221 · 512 · 19 |
Discriminant |
Eigenvalues |
2- -1 5+ -1 0 -1 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-48033,6255937] |
[a1,a2,a3,a4,a6] |
Generators |
[157:1600:1] |
Generators of the group modulo torsion |
j |
-2992209121/2375000 |
j-invariant |
L |
3.9713360061964 |
L(r)(E,1)/r! |
Ω |
0.37490098323548 |
Real period |
R |
1.3241282977984 |
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 |
30400c1 7600k1 6080p1 |
Quadratic twists by: -4 8 5 |