Atkin-Lehner |
2- 3+ 5+ 11- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
81180b |
Isogeny class |
Conductor |
81180 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
21525504 |
Modular degree for the optimal curve |
Δ |
243540000000 = 28 · 33 · 57 · 11 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 4 11- -2 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4179962088,-104017551778988] |
[a1,a2,a3,a4,a6] |
Generators |
[-219009117903549962515606493910810022617911984615794089774178015193096590662207625241992281946236080539640535585688731688335679716555831:8334307521730470040507793911525024226184207596596408790562824419588749760136126836698728499174598419862301314492216896610149595:5867277807417841262595745323516111503774365731904549455908426496476272821377832232255239022995172589310668134318512865886323566173] |
Generators of the group modulo torsion |
j |
1168522316434200561569501847552/35234375 |
j-invariant |
L |
7.4823078283267 |
L(r)(E,1)/r! |
Ω |
0.018776146665154 |
Real period |
R |
199.2503563634 |
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 |
81180c1 |
Quadratic twists by: -3 |