Properties

Label 154869n
Number of curves $6$
Conductor $154869$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("154869.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154869n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
154869.l5 154869n1 [1, 1, 0, -8671, -449456] [2] 442368 \(\Gamma_0(N)\)-optimal
154869.l4 154869n2 [1, 1, 0, -154876, -23520605] [2, 2] 884736  
154869.l3 154869n3 [1, 1, 0, -171121, -18305960] [2, 2] 1769472  
154869.l1 154869n4 [1, 1, 0, -2477911, -1502364686] [2] 1769472  
154869.l2 154869n5 [1, 1, 0, -1086256, 421507921] [2] 3538944  
154869.l6 154869n6 [1, 1, 0, 484094, -124057661] [2] 3538944  

Rank

sage: E.rank()
 

The elliptic curves in class 154869n have rank \(0\).

Modular form 154869.2.a.l

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - 2q^{5} - q^{6} - 3q^{8} + q^{9} - 2q^{10} - q^{11} + q^{12} - q^{13} + 2q^{15} - q^{16} - 6q^{17} + q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.