Properties

Label 72450bk
Number of curves $4$
Conductor $72450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72450.b4 72450bk1 [1, -1, 0, 1045008, -2896035584] [2] 5529600 \(\Gamma_0(N)\)-optimal
72450.b2 72450bk2 [1, -1, 0, -25198992, -46382343584] [2] 11059200  
72450.b3 72450bk3 [1, -1, 0, -9434367, 79561974541] [2] 16588800  
72450.b1 72450bk4 [1, -1, 0, -341210367, 2414269686541] [2] 33177600  

Rank

sage: E.rank()
 

The elliptic curves in class 72450bk have rank \(1\).

Complex multiplication

The elliptic curves in class 72450bk do not have complex multiplication.

Modular form 72450.2.a.bk

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

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.