# Properties

 Label 36784.bk Number of curves $3$ Conductor $36784$ CM no Rank $0$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 36784.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36784.bk1 36784bj3 $$[0, -1, 0, -1489429, -699148899]$$ $$-50357871050752/19$$ $$-137869963264$$ $$[]$$ $$291600$$ $$1.9255$$
36784.bk2 36784bj2 $$[0, -1, 0, -18069, -988579]$$ $$-89915392/6859$$ $$-49771056738304$$ $$[]$$ $$97200$$ $$1.3762$$
36784.bk3 36784bj1 $$[0, -1, 0, 1291, -1219]$$ $$32768/19$$ $$-137869963264$$ $$[]$$ $$32400$$ $$0.82692$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 36784.bk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 36784.bk do not have complex multiplication.

## Modular form 36784.2.a.bk

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 