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SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 378560.hv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
378560.hv1 | 378560hv1 | \([0, -1, 0, -322001, -64945999]\) | \(46689225424/3901625\) | \(308550019721216000\) | \([2]\) | \(6193152\) | \(2.0978\) | \(\Gamma_0(N)\)-optimal |
378560.hv2 | 378560hv2 | \([0, -1, 0, 340479, -298271455]\) | \(13799183324/129390625\) | \(-40930104656896000000\) | \([2]\) | \(12386304\) | \(2.4444\) |
Rank
sage: E.rank()
The elliptic curves in class 378560.hv have rank \(1\).
Complex multiplication
The elliptic curves in class 378560.hv do not have complex multiplication.Modular form 378560.2.a.hv
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.