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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 225400.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
225400.br1 | 225400ce4 | \([0, 0, 0, -4217675, -3333874250]\) | \(4407931365156/100625\) | \(189414890000000000\) | \([2]\) | \(2949120\) | \(2.4287\) | |
225400.br2 | 225400ce3 | \([0, 0, 0, -1130675, 414086750]\) | \(84923690436/9794435\) | \(18436887733040000000\) | \([2]\) | \(2949120\) | \(2.4287\) | |
225400.br3 | 225400ce2 | \([0, 0, 0, -273175, -48105750]\) | \(4790692944/648025\) | \(304957972900000000\) | \([2, 2]\) | \(1474560\) | \(2.0822\) | |
225400.br4 | 225400ce1 | \([0, 0, 0, 26950, -3987375]\) | \(73598976/276115\) | \(-8121163408750000\) | \([2]\) | \(737280\) | \(1.7356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 225400.br have rank \(0\).
Complex multiplication
The elliptic curves in class 225400.br do not have complex multiplication.Modular form 225400.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.