Properties

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

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 24150.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.bt1 24150br2 \([1, 1, 1, -9013, 320531]\) \(5182207647625/91449288\) \(1428895125000\) \([2]\) \(55296\) \(1.1286\)  
24150.bt2 24150br1 \([1, 1, 1, -13, 14531]\) \(-15625/5842368\) \(-91287000000\) \([2]\) \(27648\) \(0.78199\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24150.2.a.bt

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