Atkin-Lehner |
2+ 3- 47- |
Signs for the Atkin-Lehner involutions |
Class |
27072be |
Isogeny class |
Conductor |
27072 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-102308769792 = -1 · 212 · 312 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 2 -4 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-84,-15392] |
[a1,a2,a3,a4,a6] |
Generators |
[29:81:1] |
Generators of the group modulo torsion |
j |
-21952/34263 |
j-invariant |
L |
5.2819875165122 |
L(r)(E,1)/r! |
Ω |
0.48018444716219 |
Real period |
R |
2.7499784445997 |
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 |
27072o1 13536bd1 9024p1 |
Quadratic twists by: -4 8 -3 |