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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 350658.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350658.z1 | 350658z2 | \([1, -1, 0, -165953277, -821067141317]\) | \(391379047744832043625/964051690355138\) | \(1245041878553966961574722\) | \([2]\) | \(66355200\) | \(3.5014\) | |
350658.z2 | 350658z1 | \([1, -1, 0, -6512787, -22493503103]\) | \(-23655968592999625/155579103523228\) | \(-200925428845984009483932\) | \([2]\) | \(33177600\) | \(3.1549\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350658.z have rank \(0\).
Complex multiplication
The elliptic curves in class 350658.z do not have complex multiplication.Modular form 350658.2.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.