Atkin-Lehner |
2- 3+ 5- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
21360i |
Isogeny class |
Conductor |
21360 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
265752576000000 = 218 · 36 · 56 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 0 2 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-26960,1521600] |
[a1,a2,a3,a4,a6] |
Generators |
[170:1350:1] |
Generators of the group modulo torsion |
j |
529102162437841/64881000000 |
j-invariant |
L |
4.6346500214626 |
L(r)(E,1)/r! |
Ω |
0.53241421949459 |
Real period |
R |
0.72541420003492 |
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 |
2670e1 85440bh1 64080z1 106800br1 |
Quadratic twists by: -4 8 -3 5 |