# Properties

 Label 179520da Number of curves $2$ Conductor $179520$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("da1")

sage: E.isogeny_class()

## Elliptic curves in class 179520da

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.dy2 179520da1 [0, -1, 0, 1695, -24063]  196608 $$\Gamma_0(N)$$-optimal
179520.dy1 179520da2 [0, -1, 0, -9185, -213375]  393216

## Rank

sage: E.rank()

The elliptic curves in class 179520da have rank $$1$$.

## Complex multiplication

The elliptic curves in class 179520da do not have complex multiplication.

## Modular form 179520.2.a.da

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 2q^{7} + q^{9} + q^{11} - q^{15} + q^{17} + O(q^{20})$$

## 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. 