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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 46200.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.cr1 | 46200cu4 | \([0, 1, 0, -16005808, -17481678112]\) | \(14171198121996897746/4077720290568771\) | \(130487049298200672000000\) | \([2]\) | \(5898240\) | \(3.1419\) | |
| 46200.cr2 | 46200cu2 | \([0, 1, 0, -14674808, -21639722112]\) | \(21843440425782779332/3100814593569\) | \(49613033497104000000\) | \([2, 2]\) | \(2949120\) | \(2.7953\) | |
| 46200.cr3 | 46200cu1 | \([0, 1, 0, -14674308, -21641270112]\) | \(87364831012240243408/1760913\) | \(7043652000000\) | \([2]\) | \(1474560\) | \(2.4487\) | \(\Gamma_0(N)\)-optimal |
| 46200.cr4 | 46200cu3 | \([0, 1, 0, -13351808, -25698686112]\) | \(-8226100326647904626/4152140742401883\) | \(-132868503756860256000000\) | \([2]\) | \(5898240\) | \(3.1419\) |
Rank
sage: E.rank()
The elliptic curves in class 46200.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 46200.cr do not have complex multiplication.Modular form 46200.2.a.cr
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
