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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 262392.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262392.bv1 | 262392bv1 | \([0, 1, 0, -547771, 146417882]\) | \(1909913257984/129730653\) | \(1234669085647337808\) | \([2]\) | \(5806080\) | \(2.2200\) | \(\Gamma_0(N)\)-optimal |
262392.bv2 | 262392bv2 | \([0, 1, 0, 474044, 630758192]\) | \(77366117936/1172914587\) | \(-178605299171502957312\) | \([2]\) | \(11612160\) | \(2.5666\) |
Rank
sage: E.rank()
The elliptic curves in class 262392.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 262392.bv do not have complex multiplication.Modular form 262392.2.a.bv
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.