# Properties

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

# Related objects

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.