Atkin-Lehner |
3- 7- 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
27489r |
Isogeny class |
Conductor |
27489 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
63063060621331617 = 35 · 710 · 11 · 174 |
Discriminant |
Eigenvalues |
-1 3- -2 7- 11+ 2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-6556299,-6462078120] |
[a1,a2,a3,a4,a6] |
Generators |
[-23117775:12728037:15625] |
Generators of the group modulo torsion |
j |
264918160154242157473/536027170833 |
j-invariant |
L |
3.3329898408182 |
L(r)(E,1)/r! |
Ω |
0.094348482467646 |
Real period |
R |
7.0652749331949 |
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 |
82467bd1 3927d1 |
Quadratic twists by: -3 -7 |