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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 160113d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160113.d3 | 160113d1 | \([1, 1, 1, -4272, -94656]\) | \(389017/57\) | \(1263368584353\) | \([2]\) | \(224640\) | \(1.0470\) | \(\Gamma_0(N)\)-optimal |
| 160113.d2 | 160113d2 | \([1, 1, 1, -18317, 854786]\) | \(30664297/3249\) | \(72012009308121\) | \([2, 2]\) | \(449280\) | \(1.3936\) | |
| 160113.d1 | 160113d3 | \([1, 1, 1, -285172, 58495466]\) | \(115714886617/1539\) | \(34110951777531\) | \([2]\) | \(898560\) | \(1.7401\) | |
| 160113.d4 | 160113d4 | \([1, 1, 1, 23818, 4259294]\) | \(67419143/390963\) | \(-8665445120077227\) | \([2]\) | \(898560\) | \(1.7401\) |
Rank
sage: E.rank()
The elliptic curves in class 160113d have rank \(0\).
Complex multiplication
The elliptic curves in class 160113d do not have complex multiplication.Modular form 160113.2.a.d
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
