Properties

Label 152592.bp
Number of curves $2$
Conductor $152592$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 152592.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
152592.bp1 152592a1 [0, 1, 0, -906400, 331632884] [2] 2654208 \(\Gamma_0(N)\)-optimal
152592.bp2 152592a2 [0, 1, 0, -721440, 471092724] [2] 5308416  

Rank

sage: E.rank()
 

The elliptic curves in class 152592.bp have rank \(0\).

Complex multiplication

The elliptic curves in class 152592.bp do not have complex multiplication.

Modular form 152592.2.a.bp

sage: E.q_eigenform(10)
 
\( q + q^{3} - 4q^{5} - 2q^{7} + q^{9} + q^{11} - 4q^{15} + O(q^{20}) \)

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.