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Properties

Label 277350.bx
Number of curves $4$
Conductor $277350$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277350.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277350.bx1 277350bx4 [1, 0, 1, -38760626, -92252480602] [2] 34062336  
277350.bx2 277350bx2 [1, 0, 1, -4091876, 798444398] [2, 2] 17031168  
277350.bx3 277350bx1 [1, 0, 1, -3167376, 2166704398] [2] 8515584 \(\Gamma_0(N)\)-optimal
277350.bx4 277350bx3 [1, 0, 1, 15784874, 6284427398] [2] 34062336  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 277350.2.a.bx

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

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.