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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 2112.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2112.x1 | 2112ba1 | \([0, 1, 0, -33, -33]\) | \(62500/33\) | \(2162688\) | \([2]\) | \(256\) | \(-0.092870\) | \(\Gamma_0(N)\)-optimal |
| 2112.x2 | 2112ba2 | \([0, 1, 0, 127, -129]\) | \(1714750/1089\) | \(-142737408\) | \([2]\) | \(512\) | \(0.25370\) |
Rank
sage: E.rank()
The elliptic curves in class 2112.x have rank \(0\).
Complex multiplication
The elliptic curves in class 2112.x do not have complex multiplication.Modular form 2112.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
