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Properties

Label 24150.bm
Number of curves $2$
Conductor $24150$
CM no
Rank $1$
Graph

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

Elliptic curves in class 24150.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.bm1 24150bq1 \([1, 1, 1, -588, 2781]\) \(1439069689/579600\) \(9056250000\) \([2]\) \(18432\) \(0.60852\) \(\Gamma_0(N)\)-optimal
24150.bm2 24150bq2 \([1, 1, 1, 1912, 22781]\) \(49471280711/41992020\) \(-656125312500\) \([2]\) \(36864\) \(0.95510\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24150.bm have rank \(1\).

Complex multiplication

The elliptic curves in class 24150.bm do not have complex multiplication.

Modular form 24150.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - 2 q^{11} - q^{12} - 4 q^{13} - q^{14} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.