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SageMath
E = EllipticCurve("btz1")
E.isogeny_class()
Elliptic curves in class 705600.btz
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.btz1 | \([0, 0, 0, -401736300, -3092575122000]\) | \(551105805571803/1376829440\) | \(17913980449739243520000000\) | \([2]\) | \(247726080\) | \(3.7230\) |
705600.btz2 | \([0, 0, 0, -251208300, -5438102418000]\) | \(-134745327251163/903920796800\) | \(-11760948024170604134400000000\) | \([2]\) | \(495452160\) | \(4.0696\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.btz have rank \(0\).
Complex multiplication
The elliptic curves in class 705600.btz do not have complex multiplication.Modular form 705600.2.a.btz
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.