# Properties

 Label 327990.bp Number of curves $2$ Conductor $327990$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 327990.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.bp1 327990bp2 $$[1, 0, 0, -716970, -233727228]$$ $$68523370149961/243360$$ $$144756203398560$$ $$$$ $$3745280$$ $$1.9355$$
327990.bp2 327990bp1 $$[1, 0, 0, -44170, -3764188]$$ $$-16022066761/998400$$ $$-593871603686400$$ $$$$ $$1872640$$ $$1.5889$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 327990.bp have rank $$0$$.

## Complex multiplication

The elliptic curves in class 327990.bp do not have complex multiplication.

## Modular form 327990.2.a.bp

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} - q^{13} - 2q^{14} + q^{15} + q^{16} - 4q^{17} + q^{18} + 2q^{19} + O(q^{20})$$ ## 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. 