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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 38640.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.bg1 | 38640j4 | \([0, -1, 0, -185480, 30808272]\) | \(344577854816148242/2716875\) | \(5564160000\) | \([2]\) | \(122880\) | \(1.4609\) | |
| 38640.bg2 | 38640j2 | \([0, -1, 0, -11600, 483600]\) | \(168591300897604/472410225\) | \(483748070400\) | \([2, 2]\) | \(61440\) | \(1.1143\) | |
| 38640.bg3 | 38640j3 | \([0, -1, 0, -7000, 866320]\) | \(-18524646126002/146738831715\) | \(-300521127352320\) | \([2]\) | \(122880\) | \(1.4609\) | |
| 38640.bg4 | 38640j1 | \([0, -1, 0, -1020, 1152]\) | \(458891455696/264449745\) | \(67699134720\) | \([2]\) | \(30720\) | \(0.76776\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.bg do not have complex multiplication.Modular form 38640.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
