# Properties

 Label 1764.f Number of curves $2$ Conductor $1764$ CM -3 Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1764.f1")

sage: E.isogeny_class()

## Elliptic curves in class 1764.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1764.f1 1764a2 [0, 0, 0, 0, -259308] [] 3024
1764.f2 1764a1 [0, 0, 0, 0, 9604]  1008 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1764.2.a.f

sage: E.q_eigenform(10)

$$q + 5q^{13} - q^{19} + O(q^{20})$$

## 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. 