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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 16562.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16562.k1 | 16562l2 | \([1, 1, 0, -98361, 10763173]\) | \(2633034313/262144\) | \(10478106792165376\) | \([]\) | \(134784\) | \(1.8105\) | |
16562.k2 | 16562l1 | \([1, 1, 0, -21466, -1217068]\) | \(27369433/64\) | \(2558131541056\) | \([]\) | \(44928\) | \(1.2612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16562.k have rank \(0\).
Complex multiplication
The elliptic curves in class 16562.k do not have complex multiplication.Modular form 16562.2.a.k
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.