Atkin-Lehner |
2+ 3+ 5+ 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
83490b |
Isogeny class |
Conductor |
83490 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12386304 |
Modular degree for the optimal curve |
Δ |
2.311204110336E+21 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -2 11+ 2 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-92411068,341881227472] |
[a1,a2,a3,a4,a6] |
Generators |
[288766456:-23380794620:24389] |
Generators of the group modulo torsion |
j |
65571879529924849438074899/1736441856000000000 |
j-invariant |
L |
2.7858462564704 |
L(r)(E,1)/r! |
Ω |
0.13520886063978 |
Real period |
R |
10.302010692284 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000167 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
83490bj1 |
Quadratic twists by: -11 |