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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 46200cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46200.q2 | 46200cg1 | \([0, -1, 0, 1917, 1478412]\) | \(24918016/30255687\) | \(-945490218750000\) | \([2]\) | \(161280\) | \(1.5526\) | \(\Gamma_0(N)\)-optimal |
46200.q1 | 46200cg2 | \([0, -1, 0, -183708, 29693412]\) | \(1371324638864/34941753\) | \(17470876500000000\) | \([2]\) | \(322560\) | \(1.8991\) |
Rank
sage: E.rank()
The elliptic curves in class 46200cg have rank \(0\).
Complex multiplication
The elliptic curves in class 46200cg do not have complex multiplication.Modular form 46200.2.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.