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SageMath
E = EllipticCurve("gy1")
E.isogeny_class()
Elliptic curves in class 450800gy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.gy2 | 450800gy1 | \([0, -1, 0, 13312, 1183232]\) | \(21653735/63112\) | \(-760326521651200\) | \([]\) | \(1990656\) | \(1.5388\) | \(\Gamma_0(N)\)-optimal |
450800.gy1 | 450800gy2 | \([0, -1, 0, -123888, -38659648]\) | \(-17455277065/43606528\) | \(-525339075857612800\) | \([]\) | \(5971968\) | \(2.0881\) |
Rank
sage: E.rank()
The elliptic curves in class 450800gy have rank \(1\).
Complex multiplication
The elliptic curves in class 450800gy do not have complex multiplication.Modular form 450800.2.a.gy
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.