Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 6160.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6160.j1 | 6160g4 | \([0, -1, 0, -417856, 101158656]\) | \(1969902499564819009/63690429687500\) | \(260876000000000000\) | \([2]\) | \(82944\) | \(2.1158\) | |
| 6160.j2 | 6160g2 | \([0, -1, 0, -57216, -5201920]\) | \(5057359576472449/51765560000\) | \(212031733760000\) | \([2]\) | \(27648\) | \(1.5665\) | |
| 6160.j3 | 6160g1 | \([0, -1, 0, -896, -200704]\) | \(-19443408769/4249907200\) | \(-17407619891200\) | \([2]\) | \(13824\) | \(1.2199\) | \(\Gamma_0(N)\)-optimal |
| 6160.j4 | 6160g3 | \([0, -1, 0, 8064, 5411840]\) | \(14156681599871/3100231750000\) | \(-12698549248000000\) | \([2]\) | \(41472\) | \(1.7692\) |
Rank
sage: E.rank()
The elliptic curves in class 6160.j have rank \(1\).
Complex multiplication
The elliptic curves in class 6160.j do not have complex multiplication.Modular form 6160.2.a.j
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
