Atkin-Lehner |
2+ 3+ 17- 67- |
Signs for the Atkin-Lehner involutions |
Class |
82008d |
Isogeny class |
Conductor |
82008 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1462272 |
Modular degree for the optimal curve |
Δ |
-694518493307904 = -1 · 210 · 33 · 174 · 673 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -3 -2 0 17- -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4790691,-4035946258] |
[a1,a2,a3,a4,a6] |
Generators |
[2578:27336:1] |
Generators of the group modulo torsion |
j |
-439799235924127637484/25120026523 |
j-invariant |
L |
6.7995631555624 |
L(r)(E,1)/r! |
Ω |
0.05102347315471 |
Real period |
R |
2.7763215034695 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002807 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82008j1 |
Quadratic twists by: -3 |