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SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 5577.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 5577.g1 | 5577g4 | [1, 0, 1, -1160020, 480793679] | [2] | 43008 | |
| 5577.g2 | 5577g5 | [1, 0, 1, -508525, -135200167] | [2] | 86016 | |
| 5577.g3 | 5577g3 | [1, 0, 1, -80110, 5834051] | [2, 2] | 43008 | |
| 5577.g4 | 5577g2 | [1, 0, 1, -72505, 7507151] | [2, 2] | 21504 | |
| 5577.g5 | 5577g1 | [1, 0, 1, -4060, 142469] | [2] | 10752 | \(\Gamma_0(N)\)-optimal |
| 5577.g6 | 5577g6 | [1, 0, 1, 226625, 39820289] | [2] | 86016 |
Rank
sage: E.rank()
The elliptic curves in class 5577.g have rank \(1\).
Complex multiplication
The elliptic curves in class 5577.g do not have complex multiplication.Modular form 5577.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
