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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 318402cg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
318402.cg2 | 318402cg1 | \([1, -1, 0, 23217, 93143917]\) | \(189/512\) | \(-3749209000722630144\) | \([]\) | \(7185024\) | \(2.2430\) | \(\Gamma_0(N)\)-optimal |
318402.cg1 | 318402cg2 | \([1, -1, 0, -14835543, 21999909077]\) | \(-67645179/8\) | \(-42705833773856208984\) | \([]\) | \(21555072\) | \(2.7923\) |
Rank
sage: E.rank()
The elliptic curves in class 318402cg have rank \(0\).
Complex multiplication
The elliptic curves in class 318402cg do not have complex multiplication.Modular form 318402.2.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.