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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 11560a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11560.g3 | 11560a1 | \([0, 0, 0, -578, 4913]\) | \(55296/5\) | \(1931005520\) | \([2]\) | \(5120\) | \(0.52125\) | \(\Gamma_0(N)\)-optimal |
11560.g2 | 11560a2 | \([0, 0, 0, -2023, -29478]\) | \(148176/25\) | \(154480441600\) | \([2, 2]\) | \(10240\) | \(0.86782\) | |
11560.g1 | 11560a3 | \([0, 0, 0, -30923, -2092938]\) | \(132304644/5\) | \(123584353280\) | \([2]\) | \(20480\) | \(1.2144\) | |
11560.g4 | 11560a4 | \([0, 0, 0, 3757, -167042]\) | \(237276/625\) | \(-15448044160000\) | \([2]\) | \(20480\) | \(1.2144\) |
Rank
sage: E.rank()
The elliptic curves in class 11560a have rank \(1\).
Complex multiplication
The elliptic curves in class 11560a do not have complex multiplication.Modular form 11560.2.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.