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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 92736cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.b2 | 92736cz1 | \([0, 0, 0, -67392, -13697640]\) | \(-1679412953088/3049579729\) | \(-61465474873248768\) | \([2]\) | \(995328\) | \(1.9116\) | \(\Gamma_0(N)\)-optimal |
92736.b1 | 92736cz2 | \([0, 0, 0, -1363932, -612699120]\) | \(870143011569648/671898241\) | \(216677958903447552\) | \([2]\) | \(1990656\) | \(2.2581\) |
Rank
sage: E.rank()
The elliptic curves in class 92736cz have rank \(0\).
Complex multiplication
The elliptic curves in class 92736cz do not have complex multiplication.Modular form 92736.2.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.