# Properties

 Label 185130dn Number of curves $2$ Conductor $185130$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dn1")

sage: E.isogeny_class()

## Elliptic curves in class 185130dn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185130.cq2 185130dn1 [1, -1, 0, 28836, 1642108]  983040 $$\Gamma_0(N)$$-optimal
185130.cq1 185130dn2 [1, -1, 0, -156294, 15230650]  1966080

## Rank

sage: E.rank()

The elliptic curves in class 185130dn have rank $$1$$.

## Complex multiplication

The elliptic curves in class 185130dn do not have complex multiplication.

## Modular form 185130.2.a.dn

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} - 2q^{14} + q^{16} + q^{17} + O(q^{20})$$

## 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. 