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SageMath
sage: E = EllipticCurve("19600.dl1")
sage: E.isogeny_class()
Elliptic curves in class 19600.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 19600.dl1 | 19600cp6 | [0, -1, 0, -53518208, -150677721088] | [2] | 995328 | |
| 19600.dl2 | 19600cp5 | [0, -1, 0, -3342208, -2357465088] | [2] | 497664 | |
| 19600.dl3 | 19600cp4 | [0, -1, 0, -696208, -183041088] | [2] | 331776 | |
| 19600.dl4 | 19600cp2 | [0, -1, 0, -206208, 36086912] | [2] | 110592 | |
| 19600.dl5 | 19600cp1 | [0, -1, 0, -10208, 806912] | [2] | 55296 | \(\Gamma_0(N)\)-optimal |
| 19600.dl6 | 19600cp3 | [0, -1, 0, 87792, -16833088] | [2] | 165888 |
Rank
sage: E.rank()
The elliptic curves in class 19600.dl have rank \(1\).
Modular form 19600.2.a.dl
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
