Properties

Label 450.b
Number of curves $4$
Conductor $450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("450.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 450.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
450.b1 450c4 [1, -1, 0, -7452, -244944] [2] 640  
450.b2 450c2 [1, -1, 0, -477, 4131] [2] 128  
450.b3 450c3 [1, -1, 0, -252, -7344] [2] 320  
450.b4 450c1 [1, -1, 0, -27, 81] [2] 64 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 450.b have rank \(1\).

Modular form 450.2.a.b

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

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.

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.