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Properties

Label 76050.bx
Number of curves $2$
Conductor $76050$
CM no
Rank $0$
Graph

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

Elliptic curves in class 76050.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.bx1 76050bd2 \([1, -1, 0, -8087442, 9714812966]\) \(-1064019559329/125497034\) \(-6899873522054763656250\) \([]\) \(4609920\) \(2.9263\)  
76050.bx2 76050bd1 \([1, -1, 0, -102192, -19206784]\) \(-2146689/1664\) \(-91487337786000000\) \([]\) \(658560\) \(1.9533\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 76050.bx have rank \(0\).

Complex multiplication

The elliptic curves in class 76050.bx do not have complex multiplication.

Modular form 76050.2.a.bx

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.