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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 234650.cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234650.cg1 | 234650cg2 | \([1, 1, 0, -102257950, 397967176500]\) | \(-6434774386429585/140608\) | \(-2583995013925000000\) | \([]\) | \(37324800\) | \(3.0593\) | |
234650.cg2 | 234650cg1 | \([1, 1, 0, -1177950, 621696500]\) | \(-9836106385/3407872\) | \(-62627476787200000000\) | \([]\) | \(12441600\) | \(2.5100\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 234650.cg have rank \(1\).
Complex multiplication
The elliptic curves in class 234650.cg do not have complex multiplication.Modular form 234650.2.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 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.