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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 29008g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29008.n2 | 29008g1 | \([0, -1, 0, 768, -362032]\) | \(415292/469567\) | \(-56569946094592\) | \([2]\) | \(82944\) | \(1.3179\) | \(\Gamma_0(N)\)-optimal |
| 29008.n1 | 29008g2 | \([0, -1, 0, -71752, -7207920]\) | \(169556172914/4353013\) | \(1048837378942976\) | \([2]\) | \(165888\) | \(1.6644\) |
Rank
sage: E.rank()
The elliptic curves in class 29008g have rank \(0\).
Complex multiplication
The elliptic curves in class 29008g do not have complex multiplication.Modular form 29008.2.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.
