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Properties

Label 24150.bu
Number of curves $2$
Conductor $24150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 24150.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.bu1 24150bu1 \([1, 1, 1, -7185213, 4657416531]\) \(2625564132023811051529/918925030195200000\) \(14358203596800000000000\) \([2]\) \(1728000\) \(2.9530\) \(\Gamma_0(N)\)-optimal
24150.bu2 24150bu2 \([1, 1, 1, 21486787, 32583944531]\) \(70213095586874240921591/69970703040000000000\) \(-1093292235000000000000000\) \([2]\) \(3456000\) \(3.2995\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24150.bu have rank \(0\).

Complex multiplication

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

Modular form 24150.2.a.bu

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