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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 32490br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32490.by2 | 32490br1 | \([1, -1, 1, -734342, -249206011]\) | \(-186169411/6480\) | \(-1524350869292173680\) | \([2]\) | \(583680\) | \(2.2620\) | \(\Gamma_0(N)\)-optimal |
32490.by1 | 32490br2 | \([1, -1, 1, -11845922, -15689857579]\) | \(781484460931/900\) | \(211715398512801900\) | \([2]\) | \(1167360\) | \(2.6085\) |
Rank
sage: E.rank()
The elliptic curves in class 32490br have rank \(0\).
Complex multiplication
The elliptic curves in class 32490br 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 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.