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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 98022.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98022.g1 | 98022l1 | \([1, 0, 1, -2423, -29338]\) | \(1771561/612\) | \(543152252772\) | \([2]\) | \(237120\) | \(0.95347\) | \(\Gamma_0(N)\)-optimal |
98022.g2 | 98022l2 | \([1, 0, 1, 7187, -202318]\) | \(46268279/46818\) | \(-41551147337058\) | \([2]\) | \(474240\) | \(1.3000\) |
Rank
sage: E.rank()
The elliptic curves in class 98022.g have rank \(0\).
Complex multiplication
The elliptic curves in class 98022.g do not have complex multiplication.Modular form 98022.2.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 LMFDB 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 LMFDB labels.