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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 65520.cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65520.cz1 | 65520bh1 | \([0, 0, 0, -176907, -13482614]\) | \(820221748268836/369468094905\) | \(275806454974202880\) | \([2]\) | \(602112\) | \(2.0418\) | \(\Gamma_0(N)\)-optimal |
65520.cz2 | 65520bh2 | \([0, 0, 0, 614013, -100958366]\) | \(17147425715207422/12872524043925\) | \(-19218575417387673600\) | \([2]\) | \(1204224\) | \(2.3884\) |
Rank
sage: E.rank()
The elliptic curves in class 65520.cz have rank \(0\).
Complex multiplication
The elliptic curves in class 65520.cz do not have complex multiplication.Modular form 65520.2.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.