Properties

Label 28050.q
Number of curves 2
Conductor 28050
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28050.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28050.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28050.q1 28050c2 [1, 1, 0, -294000, 61200000] [2] 258048  
28050.q2 28050c1 [1, 1, 0, -22000, 544000] [2] 129024 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28050.q have rank \(1\).

Modular form 28050.2.a.q

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.