# Properties

 Label 1764.a Number of curves $2$ Conductor $1764$ CM no Rank $1$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 1764.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1764.a1 1764e2 $$[0, 0, 0, -62769, 6052921]$$ $$406749952$$ $$67240638864$$ $$$$ $$3780$$ $$1.3172$$
1764.a2 1764e1 $$[0, 0, 0, -1029, 2401]$$ $$1792$$ $$67240638864$$ $$[]$$ $$1260$$ $$0.76792$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1764.a have rank $$1$$.

## Complex multiplication

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

## Modular form1764.2.a.a

sage: E.q_eigenform(10)

$$q - 3q^{5} + 3q^{11} + 2q^{13} - 3q^{17} - q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 