Atkin-Lehner |
2- 3+ 5- 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
27390u |
Isogeny class |
Conductor |
27390 |
Conductor |
∏ cp |
288 |
Product of Tamagawa factors cp |
deg |
230400 |
Modular degree for the optimal curve |
Δ |
-19386335232000000 = -1 · 224 · 34 · 56 · 11 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 5- 1 11- -5 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-65830,9307427] |
[a1,a2,a3,a4,a6] |
Generators |
[-223:3711:1] |
Generators of the group modulo torsion |
j |
-31549733108459860321/19386335232000000 |
j-invariant |
L |
7.5320534337835 |
L(r)(E,1)/r! |
Ω |
0.35699364311143 |
Real period |
R |
0.073258904791156 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82170h1 |
Quadratic twists by: -3 |