Atkin-Lehner |
2- 5+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
123200ep |
Isogeny class |
Conductor |
123200 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1179648 |
Modular degree for the optimal curve |
Δ |
-555089920000000000 = -1 · 226 · 510 · 7 · 112 |
Discriminant |
Eigenvalues |
2- 2 5+ 7+ 11- 0 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,51967,-35572063] |
[a1,a2,a3,a4,a6] |
Generators |
[818728735407:-4750558936064:2857243059] |
Generators of the group modulo torsion |
j |
3789119879/135520000 |
j-invariant |
L |
9.7337652286197 |
L(r)(E,1)/r! |
Ω |
0.14033926622533 |
Real period |
R |
17.33970380515 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999994147 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
123200br1 30800be1 24640bq1 |
Quadratic twists by: -4 8 5 |