# Properties

 Label 1764.k Number of curves $2$ Conductor $1764$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 1764.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1764.k1 1764k2 $$[0, 0, 0, -16023, -778610]$$ $$20720464/63$$ $$1383235999488$$ $$$$ $$4608$$ $$1.1983$$
1764.k2 1764k1 $$[0, 0, 0, -588, -22295]$$ $$-16384/147$$ $$-201721916592$$ $$$$ $$2304$$ $$0.85170$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1764.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1764.k do not have complex multiplication.

## Modular form1764.2.a.k

sage: E.q_eigenform(10)

$$q + 4q^{5} - 2q^{11} + 6q^{13} - 4q^{17} + 4q^{19} + O(q^{20})$$ ## 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 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. 