Atkin-Lehner |
2- 3- 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
127680ey |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1580544 |
Modular degree for the optimal curve |
Δ |
-120171394560000000 = -1 · 215 · 3 · 57 · 77 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ -3 -7 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-341761,78575039] |
[a1,a2,a3,a4,a6] |
Generators |
[247:3048:1] |
Generators of the group modulo torsion |
j |
-134723250692513288/3667339921875 |
j-invariant |
L |
5.688765025243 |
L(r)(E,1)/r! |
Ω |
0.33042930541692 |
Real period |
R |
4.3040711921111 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000012913 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
127680ed1 63840bl1 |
Quadratic twists by: -4 8 |