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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 9792.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9792.bj1 | 9792bx4 | \([0, 0, 0, -65100, -4417904]\) | \(159661140625/48275138\) | \(9225522538610688\) | \([2]\) | \(55296\) | \(1.7685\) | |
| 9792.bj2 | 9792bx3 | \([0, 0, 0, -59340, -5562992]\) | \(120920208625/19652\) | \(3755555684352\) | \([2]\) | \(27648\) | \(1.4219\) | |
| 9792.bj3 | 9792bx2 | \([0, 0, 0, -24780, 1501072]\) | \(8805624625/2312\) | \(441830080512\) | \([2]\) | \(18432\) | \(1.2192\) | |
| 9792.bj4 | 9792bx1 | \([0, 0, 0, -1740, 17296]\) | \(3048625/1088\) | \(207920037888\) | \([2]\) | \(9216\) | \(0.87263\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9792.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 9792.bj do not have complex multiplication.Modular form 9792.2.a.bj
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.
