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SageMath
E = EllipticCurve("nv1")
E.isogeny_class()
Elliptic curves in class 487872.nv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.nv1 | 487872nv2 | \([0, 0, 0, -99283404, -267067279600]\) | \(1278763167594532/375974556419\) | \(31821600966188849103568896\) | \([2]\) | \(88473600\) | \(3.5994\) | \(\Gamma_0(N)\)-optimal* |
487872.nv2 | 487872nv1 | \([0, 0, 0, 16673316, -27778992208]\) | \(24226243449392/29774625727\) | \(-630013549205648809377792\) | \([2]\) | \(44236800\) | \(3.2528\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 487872.nv have rank \(1\).
Complex multiplication
The elliptic curves in class 487872.nv do not have complex multiplication.Modular form 487872.2.a.nv
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.