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Properties

Label 54150.bm
Number of curves $4$
Conductor $54150$
CM no
Rank $1$
Graph

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

Elliptic curves in class 54150.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.bm1 54150ca4 \([1, 1, 1, -4444632188, -114053575877719]\) \(13209596798923694545921/92340\) \(67878385180312500\) \([2]\) \(33177600\) \(3.7644\)  
54150.bm2 54150ca3 \([1, 1, 1, -281219188, -1735914461719]\) \(3345930611358906241/165622259047500\) \(121747579532810286679687500\) \([2]\) \(33177600\) \(3.7644\)  
54150.bm3 54150ca2 \([1, 1, 1, -277789688, -1782171557719]\) \(3225005357698077121/8526675600\) \(6267890087550056250000\) \([2, 2]\) \(16588800\) \(3.4179\)  
54150.bm4 54150ca1 \([1, 1, 1, -17147688, -28572181719]\) \(-758575480593601/40535043840\) \(-29796982012912860000000\) \([2]\) \(8294400\) \(3.0713\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 54150.2.a.bm

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.