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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 144144br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
144144.dx4 | 144144br1 | \([0, 0, 0, -2259, -348462]\) | \(-426957777/17320303\) | \(-51718147633152\) | \([2]\) | \(311296\) | \(1.3115\) | \(\Gamma_0(N)\)-optimal |
144144.dx3 | 144144br2 | \([0, 0, 0, -89379, -10227870]\) | \(26444947540257/169338169\) | \(505641063223296\) | \([2, 2]\) | \(622592\) | \(1.6581\) | |
144144.dx2 | 144144br3 | \([0, 0, 0, -144819, 3975858]\) | \(112489728522417/62811265517\) | \(187553433853513728\) | \([2]\) | \(1245184\) | \(2.0047\) | |
144144.dx1 | 144144br4 | \([0, 0, 0, -1427859, -656713710]\) | \(107818231938348177/4463459\) | \(13327817158656\) | \([2]\) | \(1245184\) | \(2.0047\) |
Rank
sage: E.rank()
The elliptic curves in class 144144br have rank \(1\).
Complex multiplication
The elliptic curves in class 144144br do not have complex multiplication.Modular form 144144.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.