Atkin-Lehner |
2- 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368cx |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
20348928 |
Modular degree for the optimal curve |
Δ |
-5.8894670446537E+22 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 11+ 13- 8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-539725356,-4826236687920] |
[a1,a2,a3,a4,a6] |
Generators |
[1217847340316856315779652802020985168808012154189491318503575641821606:519058305849346913971638360231129184247307341787035299317936063739523072:6593008062691126792931194710182984952362207298110526874332827863] |
Generators of the group modulo torsion |
j |
-3369853043629824680811/11414181695488 |
j-invariant |
L |
6.6406002940154 |
L(r)(E,1)/r! |
Ω |
0.01566124434352 |
Real period |
R |
106.0037144616 |
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 |
82368o1 20592w1 82368dh1 |
Quadratic twists by: -4 8 -3 |