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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 366300.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
366300.y1 | 366300y2 | \([0, 0, 0, -35286375, -80678659250]\) | \(1666315860501346000/40252707\) | \(117376893612000000\) | \([2]\) | \(13271040\) | \(2.7954\) | |
366300.y2 | 366300y1 | \([0, 0, 0, -2208000, -1257480875]\) | \(6532108386304000/31987847133\) | \(5829785139989250000\) | \([2]\) | \(6635520\) | \(2.4488\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 366300.y have rank \(0\).
Complex multiplication
The elliptic curves in class 366300.y do not have complex multiplication.Modular form 366300.2.a.y
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.