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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 87120cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.ci3 | 87120cy1 | \([0, 0, 0, -14883, 795938]\) | \(-1860867/320\) | \(-62694551715840\) | \([2]\) | \(207360\) | \(1.3737\) | \(\Gamma_0(N)\)-optimal |
| 87120.ci2 | 87120cy2 | \([0, 0, 0, -247203, 47306402]\) | \(8527173507/200\) | \(39184094822400\) | \([2]\) | \(414720\) | \(1.7203\) | |
| 87120.ci4 | 87120cy3 | \([0, 0, 0, 101277, -3378078]\) | \(804357/500\) | \(-71413012813824000\) | \([2]\) | \(622080\) | \(1.9230\) | |
| 87120.ci1 | 87120cy4 | \([0, 0, 0, -421443, -27527742]\) | \(57960603/31250\) | \(4463313300864000000\) | \([2]\) | \(1244160\) | \(2.2696\) |
Rank
sage: E.rank()
The elliptic curves in class 87120cy have rank \(1\).
Complex multiplication
The elliptic curves in class 87120cy do not have complex multiplication.Modular form 87120.2.a.cy
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
