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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 176610dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176610.l1 | 176610dk1 | \([1, 1, 0, -517232, 142905264]\) | \(25727239787761/11936400\) | \(7100049088784400\) | \([2]\) | \(2257920\) | \(1.9980\) | \(\Gamma_0(N)\)-optimal |
176610.l2 | 176610dk2 | \([1, 1, 0, -433132, 191027284]\) | \(-15107691357361/17809705620\) | \(-10593628242920764020\) | \([2]\) | \(4515840\) | \(2.3445\) |
Rank
sage: E.rank()
The elliptic curves in class 176610dk have rank \(0\).
Complex multiplication
The elliptic curves in class 176610dk do not have complex multiplication.Modular form 176610.2.a.dk
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.