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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 83790cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.cr2 | 83790cz1 | \([1, -1, 1, -3023, 23447]\) | \(961504803/486400\) | \(1545060787200\) | \([2]\) | \(184320\) | \(1.0314\) | \(\Gamma_0(N)\)-optimal |
83790.cr1 | 83790cz2 | \([1, -1, 1, -26543, -1641769]\) | \(651038076963/7220000\) | \(22934496060000\) | \([2]\) | \(368640\) | \(1.3780\) |
Rank
sage: E.rank()
The elliptic curves in class 83790cz have rank \(2\).
Complex multiplication
The elliptic curves in class 83790cz do not have complex multiplication.Modular form 83790.2.a.cz
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.