Properties

Label 54150.ci
Number of curves $4$
Conductor $54150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54150.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54150.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.ci1 54150ct4 [1, 0, 0, -27436188, -55316121258] [2] 3317760  
54150.ci2 54150ct3 [1, 0, 0, -1985688, -573178758] [2] 3317760  
54150.ci3 54150ct2 [1, 0, 0, -1714938, -864235008] [2, 2] 1658880  
54150.ci4 54150ct1 [1, 0, 0, -90438, -17870508] [4] 829440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54150.ci have rank \(0\).

Modular form 54150.2.a.ci

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} - 4q^{11} + q^{12} - 2q^{13} - 4q^{14} + q^{16} + 2q^{17} + q^{18} + O(q^{20}) \)

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.