Properties

Label 189525.bo
Number of curves $4$
Conductor $189525$
CM no
Rank $1$
Graph

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

Elliptic curves in class 189525.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189525.bo1 189525bi3 \([1, 0, 1, -1015501, 393771023]\) \(157551496201/13125\) \(9648081064453125\) \([2]\) \(2322432\) \(2.1110\)  
189525.bo2 189525bi2 \([1, 0, 1, -67876, 5244773]\) \(47045881/11025\) \(8104388094140625\) \([2, 2]\) \(1161216\) \(1.7644\)  
189525.bo3 189525bi1 \([1, 0, 1, -22751, -1253227]\) \(1771561/105\) \(77184648515625\) \([2]\) \(580608\) \(1.4178\) \(\Gamma_0(N)\)-optimal
189525.bo4 189525bi4 \([1, 0, 1, 157749, 32771023]\) \(590589719/972405\) \(-714807029903203125\) \([2]\) \(2322432\) \(2.1110\)  

Rank

sage: E.rank()
 

The elliptic curves in class 189525.bo have rank \(1\).

Complex multiplication

The elliptic curves in class 189525.bo do not have complex multiplication.

Modular form 189525.2.a.bo

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.