# Properties

 Label 1002.a Number of curves 2 Conductor 1002 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1002.a1")
sage: E.isogeny_class()

## Elliptic curves in class 1002.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1002.a1 1002a2 [1, 1, 0, -860, -10074] 2 384
1002.a2 1002a1 [1, 1, 0, -50, -192] 2 192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1002.a have rank $$0$$.

## Modular form1002.2.a.a

sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{12} - 4q^{13} + q^{16} + 6q^{17} - q^{18} + O(q^{20})$$

## 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. 