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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 154560bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.ek6 | 154560bx1 | \([0, 1, 0, 9219, -102861]\) | \(84611246065664/53699121315\) | \(-54987900226560\) | \([2]\) | \(458752\) | \(1.3255\) | \(\Gamma_0(N)\)-optimal |
| 154560.ek5 | 154560bx2 | \([0, 1, 0, -38801, -880785]\) | \(394315384276816/208332909225\) | \(3413326384742400\) | \([2, 2]\) | \(917504\) | \(1.6721\) | |
| 154560.ek3 | 154560bx3 | \([0, 1, 0, -356321, 81102879]\) | \(76343005935514084/694180580625\) | \(45493818531840000\) | \([2, 2]\) | \(1835008\) | \(2.0187\) | |
| 154560.ek2 | 154560bx4 | \([0, 1, 0, -489601, -131883265]\) | \(198048499826486404/242568272835\) | \(15896954328514560\) | \([2]\) | \(1835008\) | \(2.0187\) | |
| 154560.ek1 | 154560bx5 | \([0, 1, 0, -5688641, 5220392895]\) | \(155324313723954725282/13018359375\) | \(1706342400000000\) | \([2]\) | \(3670016\) | \(2.3652\) | |
| 154560.ek4 | 154560bx6 | \([0, 1, 0, -104321, 193847679]\) | \(-957928673903042/123339801817575\) | \(-16166394503833190400\) | \([2]\) | \(3670016\) | \(2.3652\) |
Rank
sage: E.rank()
The elliptic curves in class 154560bx have rank \(2\).
Complex multiplication
The elliptic curves in class 154560bx do not have complex multiplication.Modular form 154560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
