Properties

Label 2541l
Number of curves 6
Conductor 2541
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2541.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2541l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2541.j6 2541l1 [1, 0, 1, 118, 119] [2] 640 \(\Gamma_0(N)\)-optimal
2541.j5 2541l2 [1, 0, 1, -487, 845] [2, 2] 1280  
2541.j3 2541l3 [1, 0, 1, -4722, -124511] [2] 2560  
2541.j2 2541l4 [1, 0, 1, -5932, 175085] [2, 2] 2560  
2541.j1 2541l5 [1, 0, 1, -94867, 11238599] [2] 5120  
2541.j4 2541l6 [1, 0, 1, -4117, 284711] [2] 5120  

Rank

sage: E.rank()
 

The elliptic curves in class 2541l have rank \(0\).

Modular form 2541.2.a.j

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} + q^{7} - 3q^{8} + q^{9} - 2q^{10} - q^{12} + 2q^{13} + q^{14} - 2q^{15} - q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.