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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5929.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5929.g1 | 5929d2 | \([1, 0, 1, -177994, -28919607]\) | \(-24729001\) | \(-25219107990769\) | \([]\) | \(23760\) | \(1.6539\) | |
5929.g2 | 5929d1 | \([1, 0, 1, -124, 2055]\) | \(-121\) | \(-1722499009\) | \([]\) | \(2160\) | \(0.45499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5929.g have rank \(1\).
Complex multiplication
The elliptic curves in class 5929.g do not have complex multiplication.Modular form 5929.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.