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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 24150.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24150.bo1 | 24150bl4 | \([1, 1, 1, -75366463, 659455781]\) | \(3029968325354577848895529/1753440696000000000000\) | \(27397510875000000000000000\) | \([2]\) | \(6635520\) | \(3.5705\) | |
| 24150.bo2 | 24150bl2 | \([1, 1, 1, -51846088, 143666130281]\) | \(986396822567235411402169/6336721794060000\) | \(99011278032187500000\) | \([2]\) | \(2211840\) | \(3.0212\) | |
| 24150.bo3 | 24150bl1 | \([1, 1, 1, -3178088, 2334258281]\) | \(-227196402372228188089/19338934824115200\) | \(-302170856626800000000\) | \([2]\) | \(1105920\) | \(2.6746\) | \(\Gamma_0(N)\)-optimal |
| 24150.bo4 | 24150bl3 | \([1, 1, 1, 18841537, 94207781]\) | \(47342661265381757089751/27397579603968000000\) | \(-428087181312000000000000\) | \([2]\) | \(3317760\) | \(3.2239\) |
Rank
sage: E.rank()
The elliptic curves in class 24150.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 24150.bo do not have complex multiplication.Modular form 24150.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
