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SageMath
sage: E = EllipticCurve("8820.g1")
sage: E.isogeny_class()
Elliptic curves in class 8820.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 8820.g1 | 8820j3 | [0, 0, 0, -18228, -947023] | [2] | 12960 | |
| 8820.g2 | 8820j4 | [0, 0, 0, -16023, -1184722] | [2] | 25920 | |
| 8820.g3 | 8820j1 | [0, 0, 0, -588, 3773] | [2] | 4320 | \(\Gamma_0(N)\)-optimal |
| 8820.g4 | 8820j2 | [0, 0, 0, 1617, 25382] | [2] | 8640 |
Rank
sage: E.rank()
The elliptic curves in class 8820.g have rank \(0\).
Modular form 8820.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
