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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 99372.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99372.bg1 | 99372bo2 | \([0, 1, 0, -367124, -79442700]\) | \(109744/9\) | \(448771169548945152\) | \([2]\) | \(1451520\) | \(2.1297\) | |
| 99372.bg2 | 99372bo1 | \([0, 1, 0, -77289, 6812196]\) | \(16384/3\) | \(9349399365603024\) | \([2]\) | \(725760\) | \(1.7831\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 99372.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 99372.bg do not have complex multiplication.Modular form 99372.2.a.bg
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.
