Atkin-Lehner |
2+ 31+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
81344b |
Isogeny class |
Conductor |
81344 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
311808 |
Modular degree for the optimal curve |
Δ |
271290699776 = 212 · 312 · 413 |
Discriminant |
Eigenvalues |
2+ -2 2 -2 -6 6 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-91977,10705975] |
[a1,a2,a3,a4,a6] |
Generators |
[51:2480:1] |
Generators of the group modulo torsion |
j |
21009039924357568/66233081 |
j-invariant |
L |
4.1587860818265 |
L(r)(E,1)/r! |
Ω |
0.85408705615941 |
Real period |
R |
2.4346382798459 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999998397 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81344e1 40672c1 |
Quadratic twists by: -4 8 |