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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 364650em
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.em1 | 364650em1 | \([1, 1, 1, -986438, 322526531]\) | \(6793805286030262681/1048227429629952\) | \(16378553587968000000\) | \([2]\) | \(12042240\) | \(2.4103\) | \(\Gamma_0(N)\)-optimal |
364650.em2 | 364650em2 | \([1, 1, 1, 1717562, 1782686531]\) | \(35862531227445945959/108547797844556928\) | \(-1696059341321202000000\) | \([2]\) | \(24084480\) | \(2.7569\) |
Rank
sage: E.rank()
The elliptic curves in class 364650em have rank \(1\).
Complex multiplication
The elliptic curves in class 364650em do not have complex multiplication.Modular form 364650.2.a.em
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.