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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 149184eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 149184.bs2 | 149184eg1 | \([0, 0, 0, 564, 227824]\) | \(415292/469567\) | \(-22433912782848\) | \([2]\) | \(331776\) | \(1.2408\) | \(\Gamma_0(N)\)-optimal |
| 149184.bs1 | 149184eg2 | \([0, 0, 0, -52716, 4554160]\) | \(169556172914/4353013\) | \(415936869433344\) | \([2]\) | \(663552\) | \(1.5874\) |
Rank
sage: E.rank()
The elliptic curves in class 149184eg have rank \(1\).
Complex multiplication
The elliptic curves in class 149184eg do not have complex multiplication.Modular form 149184.2.a.eg
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.
