# Properties

 Label 164934dj Number of curves $2$ Conductor $164934$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 164934dj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
164934.bl2 164934dj1 [1, -1, 0, -5301, 121729] [2] 276480 $$\Gamma_0(N)$$-optimal
164934.bl1 164934dj2 [1, -1, 0, -80271, 8773267] [2] 552960

## Rank

sage: E.rank()

The elliptic curves in class 164934dj have rank $$1$$.

## Complex multiplication

The elliptic curves in class 164934dj do not have complex multiplication.

## Modular form 164934.2.a.dj

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2q^{5} - q^{8} - 2q^{10} + q^{11} - 4q^{13} + q^{16} + q^{17} - 2q^{19} + O(q^{20})$$

## 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.