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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 493680ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.ba1 | 493680ba1 | \([0, -1, 0, -16462816, 25715286016]\) | \(68001744211490809/1022422500\) | \(7419018553436160000\) | \([2]\) | \(23224320\) | \(2.7575\) | \(\Gamma_0(N)\)-optimal |
493680.ba2 | 493680ba2 | \([0, -1, 0, -15978816, 27297772416]\) | \(-62178675647294809/8362782148050\) | \(-60682971975604658380800\) | \([2]\) | \(46448640\) | \(3.1040\) |
Rank
sage: E.rank()
The elliptic curves in class 493680ba have rank \(1\).
Complex multiplication
The elliptic curves in class 493680ba do not have complex multiplication.Modular form 493680.2.a.ba
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.