Atkin-Lehner |
2- 3+ 5- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
4230x |
Isogeny class |
Conductor |
4230 |
Conductor |
∏ cp |
864 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-1954381824000000000 = -1 · 224 · 33 · 59 · 472 |
Discriminant |
Eigenvalues |
2- 3+ 5- -4 0 -4 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-70442,-67627159] |
[a1,a2,a3,a4,a6] |
Generators |
[471:1639:1] |
Generators of the group modulo torsion |
j |
-1431690694106609763/72384512000000000 |
j-invariant |
L |
5.1153439403818 |
L(r)(E,1)/r! |
Ω |
0.11516667520065 |
Real period |
R |
1.8507031698007 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
33840bl1 4230d3 21150j1 |
Quadratic twists by: -4 -3 5 |