Properties

Label 189630.bd
Number of curves $2$
Conductor $189630$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189630.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
189630.bd1 189630dx2 [1, -1, 0, -73107225, -240577441875] [2] 23224320  
189630.bd2 189630dx1 [1, -1, 0, -4522905, -3838086099] [2] 11612160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 189630.bd have rank \(1\).

Complex multiplication

The elliptic curves in class 189630.bd do not have complex multiplication.

Modular form 189630.2.a.bd

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 4q^{11} - 4q^{13} + q^{16} + 4q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.