# Properties

 Label 443760.bv Number of curves $2$ Conductor $443760$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bv1")

sage: E.isogeny_class()

## Elliptic curves in class 443760.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
443760.bv1 443760bv2 $$[0, 1, 0, -7026816, -6942767436]$$ $$1481933914201/53916840$$ $$1396031160708485775360$$ $$[2]$$ $$25546752$$ $$2.8271$$
443760.bv2 443760bv1 $$[0, 1, 0, -1110016, 301762484]$$ $$5841725401/1857600$$ $$48097542143272550400$$ $$[2]$$ $$12773376$$ $$2.4805$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 443760.bv1.

## Rank

sage: E.rank()

The elliptic curves in class 443760.bv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 443760.bv do not have complex multiplication.

## Modular form 443760.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2q^{7} + q^{9} + 2q^{11} - 2q^{13} - q^{15} - 4q^{17} - 6q^{19} + O(q^{20})$$

## 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.