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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 123210.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123210.br1 | 123210m4 | \([1, -1, 0, -298014, -16294330]\) | \(57960603/31250\) | \(1578162278385843750\) | \([2]\) | \(2384640\) | \(2.1830\) | |
123210.br2 | 123210m2 | \([1, -1, 0, -174804, 28173528]\) | \(8527173507/200\) | \(13854922608600\) | \([2]\) | \(794880\) | \(1.6337\) | |
123210.br3 | 123210m1 | \([1, -1, 0, -10524, 475920]\) | \(-1860867/320\) | \(-22167876173760\) | \([2]\) | \(397440\) | \(1.2871\) | \(\Gamma_0(N)\)-optimal |
123210.br4 | 123210m3 | \([1, -1, 0, 71616, -2026612]\) | \(804357/500\) | \(-25250596454173500\) | \([2]\) | \(1192320\) | \(1.8364\) |
Rank
sage: E.rank()
The elliptic curves in class 123210.br have rank \(0\).
Complex multiplication
The elliptic curves in class 123210.br do not have complex multiplication.Modular form 123210.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.