# Properties

 Label 1764.i Number of curves $2$ Conductor $1764$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1764.i1")

sage: E.isogeny_class()

## Elliptic curves in class 1764.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1764.i1 1764g2 [0, 0, 0, -399, -2842]  768
1764.i2 1764g1 [0, 0, 0, -84, 245]  384 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1764.2.a.i

sage: E.q_eigenform(10)

$$q + 2q^{5} - 2q^{11} + 4q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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. 