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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 32490.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32490.br1 | 32490bq1 | \([1, -1, 1, -117032, -17714761]\) | \(-14317849/2700\) | \(-33428747133600300\) | \([]\) | \(393984\) | \(1.8948\) | \(\Gamma_0(N)\)-optimal |
32490.br2 | 32490bq2 | \([1, -1, 1, 808933, 86734091]\) | \(4728305591/3000000\) | \(-37143052370667000000\) | \([3]\) | \(1181952\) | \(2.4441\) |
Rank
sage: E.rank()
The elliptic curves in class 32490.br have rank \(0\).
Complex multiplication
The elliptic curves in class 32490.br do not have complex multiplication.Modular form 32490.2.a.br
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.