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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 20160.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.cx1 | 20160r2 | \([0, 0, 0, -3132, 66096]\) | \(10536048/245\) | \(79009136640\) | \([2]\) | \(18432\) | \(0.87695\) | |
20160.cx2 | 20160r1 | \([0, 0, 0, -432, -1944]\) | \(442368/175\) | \(3527193600\) | \([2]\) | \(9216\) | \(0.53038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20160.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 20160.cx do not have complex multiplication.Modular form 20160.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.