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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 4560.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4560.ba1 | 4560j3 | \([0, 1, 0, -2440, -47212]\) | \(784767874322/35625\) | \(72960000\) | \([2]\) | \(3072\) | \(0.58494\) | |
4560.ba2 | 4560j4 | \([0, 1, 0, -760, 7220]\) | \(23735908082/1954815\) | \(4003461120\) | \([2]\) | \(3072\) | \(0.58494\) | |
4560.ba3 | 4560j2 | \([0, 1, 0, -160, -700]\) | \(445138564/81225\) | \(83174400\) | \([2, 2]\) | \(1536\) | \(0.23837\) | |
4560.ba4 | 4560j1 | \([0, 1, 0, 20, -52]\) | \(3286064/7695\) | \(-1969920\) | \([2]\) | \(768\) | \(-0.10820\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.ba do not have complex multiplication.Modular form 4560.2.a.ba
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.