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Properties

Label 59150.bl
Number of curves $2$
Conductor $59150$
CM no
Rank $1$
Graph

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

Elliptic curves in class 59150.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59150.bl1 59150bw2 \([1, 1, 1, -7693, -368139]\) \(-417267265/235298\) \(-28393462602050\) \([]\) \(165888\) \(1.2846\)  
59150.bl2 59150bw1 \([1, 1, 1, 757, 7041]\) \(397535/392\) \(-47302728200\) \([]\) \(55296\) \(0.73530\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 59150.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 59150.bl do not have complex multiplication.

Modular form 59150.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} - 2 q^{9} - 3 q^{11} - q^{12} + q^{14} + q^{16} - 3 q^{17} - 2 q^{18} + 7 q^{19} + O(q^{20})\) 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.