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SageMath
E = EllipticCurve("oi1")
E.isogeny_class()
Elliptic curves in class 310464.oi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.oi1 | 310464oi2 | \([0, 0, 0, -1480603404, 21928059286000]\) | \(46546832455691959/748268928\) | \(5770421294294678315728896\) | \([2]\) | \(115605504\) | \(3.8841\) | |
310464.oi2 | 310464oi1 | \([0, 0, 0, -89724684, 364431962608]\) | \(-10358806345399/1445216256\) | \(-11145066093781765526126592\) | \([2]\) | \(57802752\) | \(3.5375\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.oi have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.oi do not have complex multiplication.Modular form 310464.2.a.oi
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.