# Properties

 Label 84150bp Number of curves $2$ Conductor $84150$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 84150bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84150.co2 84150bp1 [1, -1, 0, 5958, -156384]  196608 $$\Gamma_0(N)$$-optimal
84150.co1 84150bp2 [1, -1, 0, -32292, -1418634]  393216

## Rank

sage: E.rank()

The elliptic curves in class 84150bp have rank $$1$$.

## Complex multiplication

The elliptic curves in class 84150bp do not have complex multiplication.

## Modular form 84150.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2q^{7} - q^{8} - q^{11} - 2q^{14} + q^{16} + q^{17} + O(q^{20})$$

## 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 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. 