# Properties

 Label 429.a Number of curves $2$ Conductor $429$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("429.a1")

sage: E.isogeny_class()

## Elliptic curves in class 429.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
429.a1 429a2 [1, 1, 1, -13, 8]  32
429.a2 429a1 [1, 1, 1, 2, 2]  16 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 429.a have rank $$1$$.

## Modular form429.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} + q^{6} + 3q^{8} + q^{9} + q^{11} + q^{12} + q^{13} - q^{16} - 4q^{17} - q^{18} - 8q^{19} + O(q^{20})$$

## 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. 