# Properties

 Label 38640bk Number of curves $2$ Conductor $38640$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bk1")

sage: E.isogeny_class()

## Elliptic curves in class 38640bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.m1 38640bk1 $$[0, -1, 0, -376, -1424]$$ $$1439069689/579600$$ $$2374041600$$ $$[2]$$ $$18432$$ $$0.49695$$ $$\Gamma_0(N)$$-optimal
38640.m2 38640bk2 $$[0, -1, 0, 1224, -11664]$$ $$49471280711/41992020$$ $$-171999313920$$ $$[2]$$ $$36864$$ $$0.84352$$

## Rank

sage: E.rank()

The elliptic curves in class 38640bk have rank $$1$$.

## Complex multiplication

The elliptic curves in class 38640bk do not have complex multiplication.

## Modular form 38640.2.a.bk

sage: E.q_eigenform(10)

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

## 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 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.