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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 9450.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.cz1 | 9450ch2 | \([1, -1, 1, -75980, -43170353]\) | \(-17525176203/280985600\) | \(-777746188800000000\) | \([]\) | \(155520\) | \(2.1142\) | |
9450.cz2 | 9450ch1 | \([1, -1, 1, 8395, 1548397]\) | \(212776173/3500000\) | \(-1076414062500000\) | \([]\) | \(51840\) | \(1.5649\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9450.cz have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.cz do not have complex multiplication.Modular form 9450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.