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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 406560bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
406560.bx3 | 406560bx1 | \([0, -1, 0, -107730, -13145328]\) | \(1219555693504/43758225\) | \(4961303349710400\) | \([2, 2]\) | \(2211840\) | \(1.7819\) | \(\Gamma_0(N)\)-optimal* |
406560.bx2 | 406560bx2 | \([0, -1, 0, -271080, 36382392]\) | \(2428799546888/778248135\) | \(705901590675832320\) | \([2]\) | \(4423680\) | \(2.1285\) | \(\Gamma_0(N)\)-optimal* |
406560.bx4 | 406560bx3 | \([0, -1, 0, 40495, -46673823]\) | \(1012048064/130203045\) | \(-944794159526891520\) | \([2]\) | \(4423680\) | \(2.1285\) | |
406560.bx1 | 406560bx4 | \([0, -1, 0, -1708560, -859023900]\) | \(608119035935048/826875\) | \(750008064960000\) | \([2]\) | \(4423680\) | \(2.1285\) |
Rank
sage: E.rank()
The elliptic curves in class 406560bx have rank \(0\).
Complex multiplication
The elliptic curves in class 406560bx do not have complex multiplication.Modular form 406560.2.a.bx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.