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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 8280.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8280.v1 | 8280v3 | \([0, 0, 0, -22107, -1265146]\) | \(1600610497636/9315\) | \(6953610240\) | \([2]\) | \(14336\) | \(1.0786\) | |
8280.v2 | 8280v2 | \([0, 0, 0, -1407, -19006]\) | \(1650587344/119025\) | \(22212921600\) | \([2, 2]\) | \(7168\) | \(0.73198\) | |
8280.v3 | 8280v1 | \([0, 0, 0, -282, 1469]\) | \(212629504/43125\) | \(503010000\) | \([4]\) | \(3584\) | \(0.38541\) | \(\Gamma_0(N)\)-optimal |
8280.v4 | 8280v4 | \([0, 0, 0, 1293, -83266]\) | \(320251964/4197615\) | \(-3133502807040\) | \([2]\) | \(14336\) | \(1.0786\) |
Rank
sage: E.rank()
The elliptic curves in class 8280.v have rank \(0\).
Complex multiplication
The elliptic curves in class 8280.v do not have complex multiplication.Modular form 8280.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.