# Properties

 Label 190575.bp Number of curves $4$ Conductor $190575$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 190575.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190575.bp1 190575be4 [1, -1, 1, -3063380, -2062798878]  4423680
190575.bp2 190575be2 [1, -1, 1, -204755, -27457878] [2, 2] 2211840
190575.bp3 190575be1 [1, -1, 1, -68630, 6573372]  1105920 $$\Gamma_0(N)$$-optimal
190575.bp4 190575be3 [1, -1, 1, 475870, -171750378]  4423680

## Rank

sage: E.rank()

The elliptic curves in class 190575.bp have rank $$0$$.

## Complex multiplication

The elliptic curves in class 190575.bp do not have complex multiplication.

## Modular form 190575.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + q^{7} + 3q^{8} - 6q^{13} - q^{14} - q^{16} - 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 