# Properties

 Label 1764.j Number of curves $2$ Conductor $1764$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 1764.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1764.j1 1764j2 $$[0, 0, 0, -1281, -17647]$$ $$406749952$$ $$571536$$ $$[]$$ $$540$$ $$0.34427$$
1764.j2 1764j1 $$[0, 0, 0, -21, -7]$$ $$1792$$ $$571536$$ $$[]$$ $$180$$ $$-0.20503$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1764.2.a.j

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.