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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 7488.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.bk1 | 7488bt4 | \([0, 0, 0, -11945964, 15892048208]\) | \(986551739719628473/111045168\) | \(21221062075219968\) | \([2]\) | \(245760\) | \(2.5571\) | |
| 7488.bk2 | 7488bt3 | \([0, 0, 0, -1347564, -204211888]\) | \(1416134368422073/725251155408\) | \(138597654145907294208\) | \([2]\) | \(245760\) | \(2.5571\) | |
| 7488.bk3 | 7488bt2 | \([0, 0, 0, -748524, 246985040]\) | \(242702053576633/2554695936\) | \(488209996144705536\) | \([2, 2]\) | \(122880\) | \(2.2105\) | |
| 7488.bk4 | 7488bt1 | \([0, 0, 0, -11244, 9580880]\) | \(-822656953/207028224\) | \(-39563709722394624\) | \([2]\) | \(61440\) | \(1.8640\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 7488.bk do not have complex multiplication.Modular form 7488.2.a.bk
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.
