Atkin-Lehner |
2+ 3+ 17- 29- |
Signs for the Atkin-Lehner involutions |
Class |
47328i |
Isogeny class |
Conductor |
47328 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
-2791272751976448 = -1 · 212 · 314 · 173 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ -4 1 0 -5 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-141665,-20632719] |
[a1,a2,a3,a4,a6] |
Generators |
[2825:148716:1] |
Generators of the group modulo torsion |
j |
-76763457520399936/681463074213 |
j-invariant |
L |
3.1680801560135 |
L(r)(E,1)/r! |
Ω |
0.12297692393307 |
Real period |
R |
1.073399265581 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000055 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47328q1 94656cc1 |
Quadratic twists by: -4 8 |