# Properties

 Label 122010do Number of curves 2 Conductor 122010 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("122010.dj1")
sage: E.isogeny_class()

## Elliptic curves in class 122010do

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
122010.dj1 122010do1 [1, 0, 0, -312566640, -2126999407968] 1 20885760 $$\Gamma_0(N)$$-optimal
122010.dj2 122010do2 [1, 0, 0, 975016510, -11270628771900] 7 146200320

## Rank

sage: E.rank()

The elliptic curves in class 122010do have rank $$1$$.

## Modular form 122010.2.a.dj

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} + q^{15} + q^{16} - 3q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 