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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 30912cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30912.by2 | 30912cg1 | \([0, 1, 0, -33, -59553]\) | \(-15625/5842368\) | \(-1531541716992\) | \([2]\) | \(36864\) | \(1.0170\) | \(\Gamma_0(N)\)-optimal |
30912.by1 | 30912cg2 | \([0, 1, 0, -23073, -1335969]\) | \(5182207647625/91449288\) | \(23972882153472\) | \([2]\) | \(73728\) | \(1.3636\) |
Rank
sage: E.rank()
The elliptic curves in class 30912cg have rank \(0\).
Complex multiplication
The elliptic curves in class 30912cg do not have complex multiplication.Modular form 30912.2.a.cg
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.