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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 9702.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.bu1 | 9702ca3 | \([1, -1, 1, -35510, -2556795]\) | \(57736239625/255552\) | \(21917703753792\) | \([2]\) | \(34560\) | \(1.4122\) | |
| 9702.bu2 | 9702ca4 | \([1, -1, 1, -17870, -5111067]\) | \(-7357983625/127552392\) | \(-10939673886111432\) | \([2]\) | \(69120\) | \(1.7588\) | |
| 9702.bu3 | 9702ca1 | \([1, -1, 1, -2435, 44223]\) | \(18609625/1188\) | \(101890151748\) | \([2]\) | \(11520\) | \(0.86288\) | \(\Gamma_0(N)\)-optimal |
| 9702.bu4 | 9702ca2 | \([1, -1, 1, 1975, 183579]\) | \(9938375/176418\) | \(-15130687534578\) | \([2]\) | \(23040\) | \(1.2095\) |
Rank
sage: E.rank()
The elliptic curves in class 9702.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.bu do not have complex multiplication.Modular form 9702.2.a.bu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
