Properties

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

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 76050bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.h1 76050bu1 \([1, -1, 0, -31979817, 69606955341]\) \(65787589563409/10400000\) \(571795861162500000000\) \([2]\) \(7741440\) \(2.9935\) \(\Gamma_0(N)\)-optimal
76050.h2 76050bu2 \([1, -1, 0, -28937817, 83378089341]\) \(-48743122863889/26406250000\) \(-1451825428732910156250000\) \([2]\) \(15482880\) \(3.3400\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 76050.2.a.bu

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