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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 72128.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.bg1 | 72128bw4 | \([0, 0, 0, -387884, 92961232]\) | \(209267191953/55223\) | \(1703131408498688\) | \([2]\) | \(491520\) | \(1.9070\) | |
| 72128.bg2 | 72128bw2 | \([0, 0, 0, -27244, 1070160]\) | \(72511713/25921\) | \(799429028478976\) | \([2, 2]\) | \(245760\) | \(1.5605\) | |
| 72128.bg3 | 72128bw1 | \([0, 0, 0, -11564, -466480]\) | \(5545233/161\) | \(4965397692416\) | \([2]\) | \(122880\) | \(1.2139\) | \(\Gamma_0(N)\)-optimal |
| 72128.bg4 | 72128bw3 | \([0, 0, 0, 82516, 7524048]\) | \(2014698447/1958887\) | \(-60413993723625472\) | \([2]\) | \(491520\) | \(1.9070\) |
Rank
sage: E.rank()
The elliptic curves in class 72128.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 72128.bg do not have complex multiplication.Modular form 72128.2.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.
