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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 328560.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
328560.cz1 | 328560cz2 | \([0, 1, 0, -463182440, 3835682958900]\) | \(1045706191321645729/323352324000\) | \(3398179213714737217536000\) | \([2]\) | \(78796800\) | \(3.6836\) | |
328560.cz2 | 328560cz1 | \([0, 1, 0, -25102440, 76430862900]\) | \(-166456688365729/143856000000\) | \(-1511813686448553984000000\) | \([2]\) | \(39398400\) | \(3.3370\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 328560.cz have rank \(0\).
Complex multiplication
The elliptic curves in class 328560.cz do not have complex multiplication.Modular form 328560.2.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 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.