Atkin-Lehner |
2- 3+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
4512k |
Isogeny class |
Conductor |
4512 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-243648 = -1 · 26 · 34 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -4 0 2 -4 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,10,-24] |
[a1,a2,a3,a4,a6] |
Generators |
[4:8:1] |
Generators of the group modulo torsion |
j |
1560896/3807 |
j-invariant |
L |
2.3168247911529 |
L(r)(E,1)/r! |
Ω |
1.6141070189778 |
Real period |
R |
1.4353600869787 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4512p1 9024bx1 13536j1 112800o1 |
Quadratic twists by: -4 8 -3 5 |