Properties

Label 154800.fy
Number of curves $4$
Conductor $154800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154800.fy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
154800.fy1 154800di3 [0, 0, 0, -3018675, 2004939250] [2] 3538944  
154800.fy2 154800di2 [0, 0, 0, -318675, -17360750] [2, 2] 1769472  
154800.fy3 154800di1 [0, 0, 0, -246675, -47096750] [2] 884736 \(\Gamma_0(N)\)-optimal
154800.fy4 154800di4 [0, 0, 0, 1229325, -136556750] [2] 3538944  

Rank

sage: E.rank()
 

The elliptic curves in class 154800.fy have rank \(1\).

Complex multiplication

The elliptic curves in class 154800.fy do not have complex multiplication.

Modular form 154800.2.a.fy

sage: E.q_eigenform(10)
 
\( q + 4q^{7} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.