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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 64400cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64400.cf2 | 64400cg1 | \([0, -1, 0, 6792, -435088]\) | \(21653735/63112\) | \(-100979200000000\) | \([]\) | \(207360\) | \(1.3706\) | \(\Gamma_0(N)\)-optimal |
64400.cf1 | 64400cg2 | \([0, -1, 0, -63208, 14124912]\) | \(-17455277065/43606528\) | \(-69770444800000000\) | \([]\) | \(622080\) | \(1.9199\) |
Rank
sage: E.rank()
The elliptic curves in class 64400cg have rank \(0\).
Complex multiplication
The elliptic curves in class 64400cg do not have complex multiplication.Modular form 64400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.