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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 705600.fv
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.fv1 | \([0, 0, 0, -10598700, -9445534000]\) | \(2185454/625\) | \(37654757763840000000000\) | \([2]\) | \(49545216\) | \(3.0384\) |
705600.fv2 | \([0, 0, 0, 1749300, -974806000]\) | \(19652/25\) | \(-753095155276800000000\) | \([2]\) | \(24772608\) | \(2.6919\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.fv have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.fv do not have complex multiplication.Modular form 705600.2.a.fv
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.