Atkin-Lehner |
3+ 5+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
86775b |
Isogeny class |
Conductor |
86775 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
502272 |
Modular degree for the optimal curve |
Δ |
2609762192578125 = 36 · 58 · 13 · 893 |
Discriminant |
Eigenvalues |
0 3+ 5+ -5 0 13+ -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-39783,-1799782] |
[a1,a2,a3,a4,a6] |
Generators |
[-168:337:1] [-118:1112:1] |
Generators of the group modulo torsion |
j |
445663628591104/167024780325 |
j-invariant |
L |
6.1860085064552 |
L(r)(E,1)/r! |
Ω |
0.34879140866851 |
Real period |
R |
1.477962748206 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999993191 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17355j1 |
Quadratic twists by: 5 |