Properties

Label 2850b
Number of curves $4$
Conductor $2850$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2850.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2850b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2850.a4 2850b1 [1, 1, 0, -250, 2500] [2] 2304 \(\Gamma_0(N)\)-optimal
2850.a3 2850b2 [1, 1, 0, -4750, 124000] [2, 2] 4608  
2850.a2 2850b3 [1, 1, 0, -5500, 81250] [2] 9216  
2850.a1 2850b4 [1, 1, 0, -76000, 8032750] [2] 9216  

Rank

sage: E.rank()
 

The elliptic curves in class 2850b have rank \(1\).

Modular form 2850.2.a.a

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

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 Cremona 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 Cremona labels.