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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 97344.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.dn1 | 97344em2 | \([0, 0, 0, -111540, -14201408]\) | \(10648000/117\) | \(1686294610071552\) | \([2]\) | \(344064\) | \(1.7365\) | |
| 97344.dn2 | 97344em1 | \([0, 0, 0, -12675, 193336]\) | \(1000000/507\) | \(114176197556928\) | \([2]\) | \(172032\) | \(1.3899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97344.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 97344.dn do not have complex multiplication.Modular form 97344.2.a.dn
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.
