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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 296208.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296208.br1 | 296208br4 | \([0, 0, 0, -8432162211, -298021155868766]\) | \(12534210458299016895673/315581882565708\) | \(1669381705442637495529684992\) | \([2]\) | \(353894400\) | \(4.3317\) | |
296208.br2 | 296208br2 | \([0, 0, 0, -547105251, -4282282960670]\) | \(3423676911662954233/483711578981136\) | \(2558763050961104073657483264\) | \([2, 2]\) | \(176947200\) | \(3.9851\) | |
296208.br3 | 296208br1 | \([0, 0, 0, -144262371, 600092176354]\) | \(62768149033310713/6915442583808\) | \(36581673322277396668219392\) | \([2]\) | \(88473600\) | \(3.6385\) | \(\Gamma_0(N)\)-optimal |
296208.br4 | 296208br3 | \([0, 0, 0, 892465629, -23015418822110]\) | \(14861225463775641287/51859390496937804\) | \(-274328542079623849784115511296\) | \([2]\) | \(353894400\) | \(4.3317\) |
Rank
sage: E.rank()
The elliptic curves in class 296208.br have rank \(0\).
Complex multiplication
The elliptic curves in class 296208.br do not have complex multiplication.Modular form 296208.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.