Atkin-Lehner |
2+ 3+ 7+ 13+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
86814b |
Isogeny class |
Conductor |
86814 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
336384 |
Modular degree for the optimal curve |
Δ |
-319687981117596 = -1 · 22 · 33 · 76 · 132 · 533 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ 2 13+ -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,387,-860335] |
[a1,a2,a3,a4,a6] |
Generators |
[107:577:1] [172:-2153:1] |
Generators of the group modulo torsion |
j |
237061729269/11840295596948 |
j-invariant |
L |
7.1033685283419 |
L(r)(E,1)/r! |
Ω |
0.25012732547143 |
Real period |
R |
2.3665842037155 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997217 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86814x1 |
Quadratic twists by: -3 |