Properties

Label 54450fr
Number of curves 4
Conductor 54450
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54450.gf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54450fr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54450.gf3 54450fr1 [1, -1, 1, -150305, 21193197] [2] 552960 \(\Gamma_0(N)\)-optimal
54450.gf4 54450fr2 [1, -1, 1, 121945, 89255697] [2] 1105920  
54450.gf1 54450fr3 [1, -1, 1, -2192180, -1243952553] [2] 1658880  
54450.gf2 54450fr4 [1, -1, 1, -1103180, -2481056553] [2] 3317760  

Rank

sage: E.rank()
 

The elliptic curves in class 54450fr have rank \(0\).

Modular form 54450.2.a.gf

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

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 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.