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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 350064.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.bx1 | 350064bx4 | \([0, 0, 0, -361390052739, -83620394996644478]\) | \(1748094148784980747354970849498497/887694600425282263291392\) | \(2650641873756286033671883849728\) | \([2]\) | \(1815478272\) | \(5.1704\) | |
| 350064.bx2 | 350064bx3 | \([0, 0, 0, -49435825539, 2326663485228418]\) | \(4474676144192042711273397261697/1806328356954994499451382272\) | \(5393667572613902295449836242075648\) | \([2]\) | \(1815478272\) | \(5.1704\) | |
| 350064.bx3 | 350064bx2 | \([0, 0, 0, -22709056899, -1291718705683070]\) | \(433744050935826360922067531137/9612122270219882316693504\) | \(28701643304920245079529735847936\) | \([2, 2]\) | \(907739136\) | \(4.8239\) | |
| 350064.bx4 | 350064bx1 | \([0, 0, 0, 128928381, -61870360369790]\) | \(79374649975090937760383/553856914190911653543936\) | \(-1653807884063435142895736193024\) | \([2]\) | \(453869568\) | \(4.4773\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350064.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 350064.bx do not have complex multiplication.Modular form 350064.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
