Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76050bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76050.co2 76050bl1 \([1, -1, 0, 151308, 62842716]\) \(6967871/35100\) \(-1929811031423437500\) \([2]\) \(1548288\) \(2.1909\) \(\Gamma_0(N)\)-optimal
76050.co1 76050bl2 \([1, -1, 0, -1749942, 798626466]\) \(10779215329/1232010\) \(67736367202962656250\) \([2]\) \(3096576\) \(2.5375\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 76050.2.a.bl

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