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Properties

Label 185150bo
Number of curves $2$
Conductor $185150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 185150bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.b2 185150bo1 \([1, 0, 1, -53176, -4343502]\) \(7189057/644\) \(1489611133062500\) \([2]\) \(1622016\) \(1.6512\) \(\Gamma_0(N)\)-optimal
185150.b1 185150bo2 \([1, 0, 1, -185426, 25809498]\) \(304821217/51842\) \(119913696211531250\) \([2]\) \(3244032\) \(1.9978\)  

Rank

sage: E.rank()
 

The elliptic curves in class 185150bo have rank \(1\).

Complex multiplication

The elliptic curves in class 185150bo do not have complex multiplication.

Modular form 185150.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} + q^{7} - q^{8} + q^{9} - 6 q^{11} - 2 q^{12} + 4 q^{13} - q^{14} + q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.