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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 89280.dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
89280.dm1 | 89280ch2 | \([0, 0, 0, -1159212, 168321584]\) | \(901456690969801/457629750000\) | \(87454407131136000000\) | \([2]\) | \(2949120\) | \(2.5189\) | |
89280.dm2 | 89280ch1 | \([0, 0, 0, 269268, 20331056]\) | \(11298232190519/7472736000\) | \(-1428062088462336000\) | \([2]\) | \(1474560\) | \(2.1724\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 89280.dm have rank \(1\).
Complex multiplication
The elliptic curves in class 89280.dm do not have complex multiplication.Modular form 89280.2.a.dm
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.