Properties

Label 24150bs
Number of curves $4$
Conductor $24150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 24150bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.ca3 24150bs1 \([1, 1, 1, -8838, -323469]\) \(4886171981209/270480\) \(4226250000\) \([2]\) \(36864\) \(0.91258\) \(\Gamma_0(N)\)-optimal
24150.ca2 24150bs2 \([1, 1, 1, -9338, -285469]\) \(5763259856089/1143116100\) \(17861189062500\) \([2, 2]\) \(73728\) \(1.2591\)  
24150.ca4 24150bs3 \([1, 1, 1, 19412, -1665469]\) \(51774168853511/107398242630\) \(-1678097541093750\) \([2]\) \(147456\) \(1.6057\)  
24150.ca1 24150bs4 \([1, 1, 1, -46088, 3536531]\) \(692895692874169/51420783750\) \(803449746093750\) \([2]\) \(147456\) \(1.6057\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24150.2.a.bs

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.