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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2280a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2280.b4 | 2280a1 | \([0, -1, 0, 20, 52]\) | \(3286064/7695\) | \(-1969920\) | \([2]\) | \(384\) | \(-0.10820\) | \(\Gamma_0(N)\)-optimal |
2280.b3 | 2280a2 | \([0, -1, 0, -160, 700]\) | \(445138564/81225\) | \(83174400\) | \([2, 2]\) | \(768\) | \(0.23837\) | |
2280.b2 | 2280a3 | \([0, -1, 0, -760, -7220]\) | \(23735908082/1954815\) | \(4003461120\) | \([2]\) | \(1536\) | \(0.58494\) | |
2280.b1 | 2280a4 | \([0, -1, 0, -2440, 47212]\) | \(784767874322/35625\) | \(72960000\) | \([2]\) | \(1536\) | \(0.58494\) |
Rank
sage: E.rank()
The elliptic curves in class 2280a have rank \(0\).
Complex multiplication
The elliptic curves in class 2280a do not have complex multiplication.Modular form 2280.2.a.a
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.