# Properties

 Label 1005a Number of curves 2 Conductor 1005 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1005.b1")

sage: E.isogeny_class()

## Elliptic curves in class 1005a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1005.b1 1005a1 [1, 1, 0, -297, -1944]  360 $$\Gamma_0(N)$$-optimal
1005.b2 1005a2 [1, 1, 0, 328, -8319]  720

## Rank

sage: E.rank()

The elliptic curves in class 1005a have rank $$0$$.

## Modular form1005.2.a.b

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 3q^{8} + q^{9} + q^{10} + q^{12} + 4q^{13} - q^{15} - q^{16} - 4q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 