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Properties

Label 5850.bx
Number of curves $2$
Conductor $5850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 5850.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bx1 5850bi2 \([1, -1, 1, -9830, -372653]\) \(-8538302475/26\) \(-319848750\) \([]\) \(7776\) \(0.85914\)  
5850.bx2 5850bi1 \([1, -1, 1, -80, -853]\) \(-3316275/17576\) \(-296595000\) \([3]\) \(2592\) \(0.30983\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.bx have rank \(0\).

Complex multiplication

The elliptic curves in class 5850.bx do not have complex multiplication.

Modular form 5850.2.a.bx

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.