Properties

Label 277350.bu
Number of curves $2$
Conductor $277350$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277350.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.bu1 277350bu2 \([1, 0, 1, -44501, 4223648]\) \(-337335507529/72000000\) \(-2080125000000000\) \([]\) \(1741824\) \(1.6606\)  
277350.bu2 277350bu1 \([1, 0, 1, 3874, -33352]\) \(222641831/145800\) \(-4212253125000\) \([]\) \(580608\) \(1.1113\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 277350.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 277350.bu do not have complex multiplication.

Modular form 277350.2.a.bu

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 2q^{7} - q^{8} + q^{9} - 3q^{11} + q^{12} + 4q^{13} - 2q^{14} + q^{16} + 3q^{17} - q^{18} + q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.