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Properties

Label 54150bw
Number of curves $2$
Conductor $54150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 54150bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.cd2 54150bw1 \([1, 1, 1, -188, 2412281]\) \(-1/3420\) \(-2514014265937500\) \([2]\) \(414720\) \(1.6339\) \(\Gamma_0(N)\)-optimal
54150.cd1 54150bw2 \([1, 1, 1, -270938, 53313281]\) \(2992209121/54150\) \(39805225877343750\) \([2]\) \(829440\) \(1.9805\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54150bw have rank \(1\).

Complex multiplication

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

Modular form 54150.2.a.bw

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.