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Properties

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

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 59150bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59150.f1 59150bb1 \([1, 0, 1, -8961, 222068]\) \(131872229/40768\) \(24597418664000\) \([2]\) \(193536\) \(1.2740\) \(\Gamma_0(N)\)-optimal
59150.f2 59150bb2 \([1, 0, 1, 24839, 1506468]\) \(2809189531/3246152\) \(-1958569461121000\) \([2]\) \(387072\) \(1.6206\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 59150.2.a.bb

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