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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 20160eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.cq3 | 20160eg1 | \([0, 0, 0, -2568, -48008]\) | \(2508888064/118125\) | \(88179840000\) | \([2]\) | \(24576\) | \(0.86102\) | \(\Gamma_0(N)\)-optimal |
| 20160.cq2 | 20160eg2 | \([0, 0, 0, -7068, 166192]\) | \(3269383504/893025\) | \(10666233446400\) | \([2, 2]\) | \(49152\) | \(1.2076\) | |
| 20160.cq1 | 20160eg3 | \([0, 0, 0, -104268, 12957712]\) | \(2624033547076/324135\) | \(15485790781440\) | \([2]\) | \(98304\) | \(1.5542\) | |
| 20160.cq4 | 20160eg4 | \([0, 0, 0, 18132, 1083472]\) | \(13799183324/18600435\) | \(-888649620848640\) | \([2]\) | \(98304\) | \(1.5542\) |
Rank
sage: E.rank()
The elliptic curves in class 20160eg have rank \(0\).
Complex multiplication
The elliptic curves in class 20160eg do not have complex multiplication.Modular form 20160.2.a.eg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
