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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 705600.u
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.u1 | \([0, 0, 0, -4577580, -3767374800]\) | \(139798359/98\) | \(7436276733247488000\) | \([2]\) | \(21233664\) | \(2.5574\) |
705600.u2 | \([0, 0, 0, -343980, -33339600]\) | \(59319/28\) | \(2124650495213568000\) | \([2]\) | \(10616832\) | \(2.2108\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.u have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.u do not have complex multiplication.Modular form 705600.2.a.u
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.