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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 40560br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.bc3 | 40560br1 | \([0, -1, 0, -16280, -5126928]\) | \(-24137569/561600\) | \(-11103174387302400\) | \([2]\) | \(193536\) | \(1.7596\) | \(\Gamma_0(N)\)-optimal |
| 40560.bc2 | 40560br2 | \([0, -1, 0, -557080, -159146768]\) | \(967068262369/4928040\) | \(97430355248578560\) | \([2]\) | \(387072\) | \(2.1061\) | |
| 40560.bc4 | 40560br3 | \([0, -1, 0, 145960, 135567600]\) | \(17394111071/411937500\) | \(-8144255518464000000\) | \([2]\) | \(580608\) | \(2.3089\) | |
| 40560.bc1 | 40560br4 | \([0, -1, 0, -3234040, 2125711600]\) | \(189208196468929/10860320250\) | \(214715152488784896000\) | \([2]\) | \(1161216\) | \(2.6554\) |
Rank
sage: E.rank()
The elliptic curves in class 40560br have rank \(1\).
Complex multiplication
The elliptic curves in class 40560br do not have complex multiplication.Modular form 40560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
