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SageMath
E = EllipticCurve("dz1")
E.isogeny_class()
Elliptic curves in class 350658dz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350658.dz2 | 350658dz1 | \([1, -1, 1, -4379, 103623]\) | \(7189057/644\) | \(831705372036\) | \([2]\) | \(622080\) | \(1.0270\) | \(\Gamma_0(N)\)-optimal |
350658.dz1 | 350658dz2 | \([1, -1, 1, -15269, -606405]\) | \(304821217/51842\) | \(66952282448898\) | \([2]\) | \(1244160\) | \(1.3736\) |
Rank
sage: E.rank()
The elliptic curves in class 350658dz have rank \(0\).
Complex multiplication
The elliptic curves in class 350658dz do not have complex multiplication.Modular form 350658.2.a.dz
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.