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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 271440ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.ds1 | 271440ds1 | \([0, 0, 0, -71787, 7388314]\) | \(13701674594089/31758480\) | \(94830313144320\) | \([2]\) | \(1081344\) | \(1.5626\) | \(\Gamma_0(N)\)-optimal |
271440.ds2 | 271440ds2 | \([0, 0, 0, -45867, 12795226]\) | \(-3573857582569/21617820900\) | \(-64550467322265600\) | \([2]\) | \(2162688\) | \(1.9092\) |
Rank
sage: E.rank()
The elliptic curves in class 271440ds have rank \(0\).
Complex multiplication
The elliptic curves in class 271440ds do not have complex multiplication.Modular form 271440.2.a.ds
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.