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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 2880bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.bg3 | 2880bg1 | \([0, 0, 0, -72, 216]\) | \(55296/5\) | \(3732480\) | \([2]\) | \(512\) | \(0.00051877\) | \(\Gamma_0(N)\)-optimal |
2880.bg2 | 2880bg2 | \([0, 0, 0, -252, -1296]\) | \(148176/25\) | \(298598400\) | \([2, 2]\) | \(1024\) | \(0.34709\) | |
2880.bg1 | 2880bg3 | \([0, 0, 0, -3852, -92016]\) | \(132304644/5\) | \(238878720\) | \([2]\) | \(2048\) | \(0.69367\) | |
2880.bg4 | 2880bg4 | \([0, 0, 0, 468, -7344]\) | \(237276/625\) | \(-29859840000\) | \([2]\) | \(2048\) | \(0.69367\) |
Rank
sage: E.rank()
The elliptic curves in class 2880bg have rank \(0\).
Complex multiplication
The elliptic curves in class 2880bg do not have complex multiplication.Modular form 2880.2.a.bg
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.