Atkin-Lehner |
2+ 3+ 5- 23- |
Signs for the Atkin-Lehner involutions |
Class |
33120d |
Isogeny class |
Conductor |
33120 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-44064883224000 = -1 · 26 · 39 · 53 · 234 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 2 -2 -4 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8397,435564] |
[a1,a2,a3,a4,a6] |
Generators |
[73:460:1] |
Generators of the group modulo torsion |
j |
-51978639168/34980125 |
j-invariant |
L |
6.375720392002 |
L(r)(E,1)/r! |
Ω |
0.59106073863717 |
Real period |
R |
0.8989093640222 |
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 |
33120z1 66240i1 33120v1 |
Quadratic twists by: -4 8 -3 |