Atkin-Lehner |
2+ 3+ 5+ 11+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
19470d |
Isogeny class |
Conductor |
19470 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7168 |
Modular degree for the optimal curve |
Δ |
2336400 = 24 · 32 · 52 · 11 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -4 11+ -6 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-33,-27] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:9:1] [-2:7:1] |
Generators of the group modulo torsion |
j |
4165509529/2336400 |
j-invariant |
L |
4.0432080005924 |
L(r)(E,1)/r! |
Ω |
2.1331656847869 |
Real period |
R |
0.94770135049237 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999984 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
58410bq1 97350cp1 |
Quadratic twists by: -3 5 |