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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 96600.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.bo1 | 96600be4 | \([0, 1, 0, -340408, 76288688]\) | \(136324616160098/88149915\) | \(2820797280000000\) | \([2]\) | \(786432\) | \(1.9049\) | |
| 96600.bo2 | 96600be2 | \([0, 1, 0, -25408, 688688]\) | \(113378906596/52490025\) | \(839840400000000\) | \([2, 2]\) | \(393216\) | \(1.5583\) | |
| 96600.bo3 | 96600be1 | \([0, 1, 0, -12908, -561312]\) | \(59466754384/905625\) | \(3622500000000\) | \([2]\) | \(196608\) | \(1.2117\) | \(\Gamma_0(N)\)-optimal |
| 96600.bo4 | 96600be3 | \([0, 1, 0, 89592, 5288688]\) | \(2485287189502/1811590515\) | \(-57970896480000000\) | \([2]\) | \(786432\) | \(1.9049\) |
Rank
sage: E.rank()
The elliptic curves in class 96600.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 96600.bo do not have complex multiplication.Modular form 96600.2.a.bo
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.
