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SageMath
E = EllipticCurve("nv1")
E.isogeny_class()
Elliptic curves in class 479808nv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.nv2 | 479808nv1 | \([0, 0, 0, -607404, 255548720]\) | \(-1102302937/616896\) | \(-13869718432754171904\) | \([2]\) | \(7077888\) | \(2.3763\) | \(\Gamma_0(N)\)-optimal* |
479808.nv1 | 479808nv2 | \([0, 0, 0, -10768044, 13598501168]\) | \(6141556990297/1019592\) | \(22923562409690923008\) | \([2]\) | \(14155776\) | \(2.7229\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479808nv have rank \(0\).
Complex multiplication
The elliptic curves in class 479808nv do not have complex multiplication.Modular form 479808.2.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 Cremona 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 Cremona labels.