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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 444360.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444360.bo1 | 444360bo3 | \([0, 1, 0, -98119096, 374059293104]\) | \(344577854816148242/2716875\) | \(823695372138240000\) | \([2]\) | \(32440320\) | \(3.0287\) | \(\Gamma_0(N)\)-optimal* |
444360.bo2 | 444360bo2 | \([0, 1, 0, -6136576, 5834869040]\) | \(168591300897604/472410225\) | \(71612075653698585600\) | \([2, 2]\) | \(16220160\) | \(2.6821\) | \(\Gamma_0(N)\)-optimal* |
444360.bo3 | 444360bo4 | \([0, 1, 0, -3703176, 10510890480]\) | \(-18524646126002/146738831715\) | \(-44487912250882907412480\) | \([2]\) | \(32440320\) | \(3.0287\) | |
444360.bo4 | 444360bo1 | \([0, 1, 0, -539756, 9698784]\) | \(458891455696/264449745\) | \(10021901592805966080\) | \([2]\) | \(8110080\) | \(2.3355\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 444360.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 444360.bo do not have complex multiplication.Modular form 444360.2.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.