Properties

Label 57154n
Number of curves 4
Conductor 57154
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("57154.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 57154n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
57154.o4 57154n1 [1, 1, 1, -5078, 84115] [2] 138240 \(\Gamma_0(N)\)-optimal
57154.o3 57154n2 [1, 1, 1, -72318, 7453619] [2] 276480  
57154.o2 57154n3 [1, 1, 1, -173178, -27807037] [2] 414720  
57154.o1 57154n4 [1, 1, 1, -189988, -22105085] [2] 829440  

Rank

sage: E.rank()
 

The elliptic curves in class 57154n have rank \(1\).

Modular form 57154.2.a.o

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.