Atkin-Lehner |
2- 3+ 37- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
83472n |
Isogeny class |
Conductor |
83472 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
823680 |
Modular degree for the optimal curve |
Δ |
-10336732453011456 = -1 · 225 · 311 · 37 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -3 2 4 -2 5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-268992,-53830656] |
[a1,a2,a3,a4,a6] |
Generators |
[749240079126:6188051553002:1187648379] |
Generators of the group modulo torsion |
j |
-525513008099696833/2523616321536 |
j-invariant |
L |
4.2066882593818 |
L(r)(E,1)/r! |
Ω |
0.10478758419121 |
Real period |
R |
20.072455586464 |
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 |
10434k1 |
Quadratic twists by: -4 |