Atkin-Lehner |
2+ 3+ 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
128832a |
Isogeny class |
Conductor |
128832 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
13176586149433344 = 212 · 310 · 114 · 612 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 11+ -6 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-59049,59049] |
[a1,a2,a3,a4,a6] |
Generators |
[-241:484:1] |
Generators of the group modulo torsion |
j |
5559154710265792/3216939977889 |
j-invariant |
L |
1.8509263253924 |
L(r)(E,1)/r! |
Ω |
0.33672715453207 |
Real period |
R |
2.7484065803828 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000382367 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
128832t2 64416c1 |
Quadratic twists by: -4 8 |