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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 20230g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20230.g2 | 20230g1 | \([1, -1, 0, -41959, -14803587]\) | \(-338463151209/3731840000\) | \(-90077545496960000\) | \([2]\) | \(138240\) | \(1.9353\) | \(\Gamma_0(N)\)-optimal |
20230.g1 | 20230g2 | \([1, -1, 0, -1197959, -502866787]\) | \(7876916680687209/27200448800\) | \(656552709740967200\) | \([2]\) | \(276480\) | \(2.2819\) |
Rank
sage: E.rank()
The elliptic curves in class 20230g have rank \(0\).
Complex multiplication
The elliptic curves in class 20230g do not have complex multiplication.Modular form 20230.2.a.g
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.