Properties

Label 54208.bl
Number of curves $4$
Conductor $54208$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54208.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54208.bl1 54208be4 [0, 0, 0, -144716, -21189520] [2] 163840  
54208.bl2 54208be3 [0, 0, 0, -28556, 1469424] [2] 163840  
54208.bl3 54208be2 [0, 0, 0, -9196, -319440] [2, 2] 81920  
54208.bl4 54208be1 [0, 0, 0, 484, -21296] [2] 40960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54208.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 54208.bl do not have complex multiplication.

Modular form 54208.2.a.bl

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.