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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 20160eo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.dp3 | 20160eo1 | \([0, 0, 0, -1452, 20176]\) | \(1771561/105\) | \(20065812480\) | \([2]\) | \(16384\) | \(0.72992\) | \(\Gamma_0(N)\)-optimal |
| 20160.dp2 | 20160eo2 | \([0, 0, 0, -4332, -84656]\) | \(47045881/11025\) | \(2106910310400\) | \([2, 2]\) | \(32768\) | \(1.0765\) | |
| 20160.dp1 | 20160eo3 | \([0, 0, 0, -64812, -6350384]\) | \(157551496201/13125\) | \(2508226560000\) | \([2]\) | \(65536\) | \(1.4231\) | |
| 20160.dp4 | 20160eo4 | \([0, 0, 0, 10068, -528176]\) | \(590589719/972405\) | \(-185829489377280\) | \([2]\) | \(65536\) | \(1.4231\) |
Rank
sage: E.rank()
The elliptic curves in class 20160eo have rank \(0\).
Complex multiplication
The elliptic curves in class 20160eo do not have complex multiplication.Modular form 20160.2.a.eo
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.
