Atkin-Lehner |
2+ 3+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
4512b |
Isogeny class |
Conductor |
4512 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
960 |
Modular degree for the optimal curve |
Δ |
-2192832 = -1 · 26 · 36 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 2 4 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2,72] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:8:1] |
Generators of the group modulo torsion |
j |
-21952/34263 |
j-invariant |
L |
3.3178491217086 |
L(r)(E,1)/r! |
Ω |
2.094751953454 |
Real period |
R |
1.5838863958273 |
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 |
4512r1 9024p1 13536bd1 112800cf1 |
Quadratic twists by: -4 8 -3 5 |