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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 480960.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480960.cz1 | 480960cz2 | \([0, 0, 0, -12184428, 15713257552]\) | \(1046819248735488409/47650971093750\) | \(9106242385305600000000\) | \([2]\) | \(33030144\) | \(2.9756\) | \(\Gamma_0(N)\)-optimal* |
480960.cz2 | 480960cz1 | \([0, 0, 0, 412692, 934316368]\) | \(40675641638471/1996889557500\) | \(-381611537181573120000\) | \([2]\) | \(16515072\) | \(2.6290\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 480960.cz have rank \(0\).
Complex multiplication
The elliptic curves in class 480960.cz do not have complex multiplication.Modular form 480960.2.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.