Properties

Label 54150.cn
Number of curves $2$
Conductor $54150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 54150.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.cn1 54150cm2 \([1, 0, 0, -288403088, 1887201522042]\) \(-27692833539889/35156250\) \(-3367895283215881347656250\) \([]\) \(17729280\) \(3.6147\)  
54150.cn2 54150cm1 \([1, 0, 0, 4819162, 12045233292]\) \(129205871/729000\) \(-69836676592764515625000\) \([]\) \(5909760\) \(3.0654\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 54150.cn do not have complex multiplication.

Modular form 54150.2.a.cn

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.