Atkin-Lehner |
2- 3+ 5+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
68160cc |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1548288 |
Modular degree for the optimal curve |
Δ |
-3560867616522240000 = -1 · 224 · 314 · 54 · 71 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -2 -6 -4 -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-314081,113386881] |
[a1,a2,a3,a4,a6] |
Generators |
[-179:12800:1] |
Generators of the group modulo torsion |
j |
-13071040729863481/13583631960000 |
j-invariant |
L |
1.802458071446 |
L(r)(E,1)/r! |
Ω |
0.22719344935884 |
Real period |
R |
1.9833957321184 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000842 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160w1 17040bb1 |
Quadratic twists by: -4 8 |