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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 32064.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32064.q1 | 32064w2 | \([0, 1, 0, -20513, 1123551]\) | \(14566408766500/6777027\) | \(444139241472\) | \([2]\) | \(56320\) | \(1.1912\) | |
32064.q2 | 32064w1 | \([0, 1, 0, -1073, 23247]\) | \(-8346562000/9861183\) | \(-161565622272\) | \([2]\) | \(28160\) | \(0.84463\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32064.q have rank \(2\).
Complex multiplication
The elliptic curves in class 32064.q do not have complex multiplication.Modular form 32064.2.a.q
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.