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SageMath
sage: E = EllipticCurve("i1")
sage: E.isogeny_class()
Elliptic curves in class 23520.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
23520.i1 | 23520bb4 | [0, -1, 0, -23536, 1397656] | [2] | 36864 | |
23520.i2 | 23520bb3 | [0, -1, 0, -3936, -65484] | [2] | 36864 | |
23520.i3 | 23520bb1 | [0, -1, 0, -1486, 21736] | [2, 2] | 18432 | \(\Gamma_0(N)\)-optimal |
23520.i4 | 23520bb2 | [0, -1, 0, 719, 78625] | [2] | 36864 |
Rank
sage: E.rank()
The elliptic curves in class 23520.i have rank \(1\).
Complex multiplication
The elliptic curves in class 23520.i do not have complex multiplication.Modular form 23520.2.a.i
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.