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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 32487.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32487.c1 | 32487b1 | \([1, 1, 1, -22296, -1290024]\) | \(10418796526321/6390657\) | \(751854405393\) | \([2]\) | \(107520\) | \(1.2216\) | \(\Gamma_0(N)\)-optimal |
32487.c2 | 32487b2 | \([1, 1, 1, -18131, -1781494]\) | \(-5602762882081/8312741073\) | \(-977985674497377\) | \([2]\) | \(215040\) | \(1.5682\) |
Rank
sage: E.rank()
The elliptic curves in class 32487.c have rank \(0\).
Complex multiplication
The elliptic curves in class 32487.c do not have complex multiplication.Modular form 32487.2.a.c
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.