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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 120384.dm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120384.dm1 | 120384b1 | \([0, 0, 0, -11916, 501488]\) | \(-26436959739/50578\) | \(-357985419264\) | \([]\) | \(276480\) | \(1.1065\) | \(\Gamma_0(N)\)-optimal |
| 120384.dm2 | 120384b2 | \([0, 0, 0, 19764, 2462832]\) | \(165469149/603592\) | \(-3114402142224384\) | \([]\) | \(829440\) | \(1.6558\) |
Rank
sage: E.rank()
The elliptic curves in class 120384.dm have rank \(1\).
Complex multiplication
The elliptic curves in class 120384.dm do not have complex multiplication.Modular form 120384.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
