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Properties

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

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 54150bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.bz1 54150bm1 \([1, 1, 1, -325088, 82012781]\) \(-14317849/2700\) \(-716494065792187500\) \([]\) \(1181952\) \(2.1502\) \(\Gamma_0(N)\)-optimal
54150.bz2 54150bm2 \([1, 1, 1, 2247037, -401546719]\) \(4728305591/3000000\) \(-796104517546875000000\) \([]\) \(3545856\) \(2.6995\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 54150.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} + 6 q^{11} - q^{12} - 5 q^{13} + q^{14} + q^{16} + q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.