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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 202800ey
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.bf2 | 202800ey1 | \([0, -1, 0, -6088, 397552]\) | \(-110940205/236196\) | \(-53137675468800\) | \([]\) | \(691200\) | \(1.3226\) | \(\Gamma_0(N)\)-optimal |
202800.bf1 | 202800ey2 | \([0, -1, 0, -165208, -50371088]\) | \(-5674525/9216\) | \(-809902080000000000\) | \([]\) | \(3456000\) | \(2.1273\) |
Rank
sage: E.rank()
The elliptic curves in class 202800ey have rank \(1\).
Complex multiplication
The elliptic curves in class 202800ey do not have complex multiplication.Modular form 202800.2.a.ey
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.