# Properties

 Label 1764.g Number of curves 4 Conductor 1764 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1764.g1")

sage: E.isogeny_class()

## Elliptic curves in class 1764.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1764.g1 1764f4 [0, 0, 0, -806295, -278668978]  13824
1764.g2 1764f3 [0, 0, 0, -49980, -4429159]  6912
1764.g3 1764f2 [0, 0, 0, -12495, -172186]  4608
1764.g4 1764f1 [0, 0, 0, 2940, -20923]  2304 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1764.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 