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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 116032.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116032.z1 | 116032be1 | \([0, 0, 0, -1960, 24696]\) | \(6912000/1813\) | \(218416780288\) | \([2]\) | \(86016\) | \(0.88462\) | \(\Gamma_0(N)\)-optimal |
116032.z2 | 116032be2 | \([0, 0, 0, 4900, 159152]\) | \(6750000/9583\) | \(-18471819132928\) | \([2]\) | \(172032\) | \(1.2312\) |
Rank
sage: E.rank()
The elliptic curves in class 116032.z have rank \(0\).
Complex multiplication
The elliptic curves in class 116032.z do not have complex multiplication.Modular form 116032.2.a.z
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.