Atkin-Lehner |
2+ 3- 5+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
31680z |
Isogeny class |
Conductor |
31680 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
-205286400 = -1 · 210 · 36 · 52 · 11 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11- 4 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,72,648] |
[a1,a2,a3,a4,a6] |
Generators |
[6:36:1] |
Generators of the group modulo torsion |
j |
55296/275 |
j-invariant |
L |
5.1020641089602 |
L(r)(E,1)/r! |
Ω |
1.2811131601137 |
Real period |
R |
0.99563103943671 |
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 |
31680cl1 3960i1 3520i1 |
Quadratic twists by: -4 8 -3 |