# Properties

 Label 39984bs Number of curves $4$ Conductor $39984$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

## Elliptic curves in class 39984bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39984.bl4 39984bs1 $$[0, -1, 0, 768, 2211840]$$ $$103823/4386816$$ $$-2113964095832064$$ $$[2]$$ $$221184$$ $$1.6195$$ $$\Gamma_0(N)$$-optimal
39984.bl3 39984bs2 $$[0, -1, 0, -250112, 47370240]$$ $$3590714269297/73410624$$ $$35375867916189696$$ $$[2, 2]$$ $$442368$$ $$1.9661$$
39984.bl2 39984bs3 $$[0, -1, 0, -532352, -78847488]$$ $$34623662831857/14438442312$$ $$6957745355016142848$$ $$[2]$$ $$884736$$ $$2.3127$$
39984.bl1 39984bs4 $$[0, -1, 0, -3981952, 3059711488]$$ $$14489843500598257/6246072$$ $$3009921534885888$$ $$[2]$$ $$884736$$ $$2.3127$$

## Rank

sage: E.rank()

The elliptic curves in class 39984bs have rank $$1$$.

## Complex multiplication

The elliptic curves in class 39984bs do not have complex multiplication.

## Modular form 39984.2.a.bs

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.