# Properties

 Label 185130.ec Number of curves 2 Conductor 185130 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("185130.ec1")

sage: E.isogeny_class()

## Elliptic curves in class 185130.ec

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185130.ec1 185130bl2 [1, -1, 1, -12806663, 17633175167] [2] 10321920
185130.ec2 185130bl1 [1, -1, 1, -958343, 159272831] [2] 5160960 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 185130.2.a.ec

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 2q^{7} + q^{8} - q^{10} + 4q^{13} + 2q^{14} + q^{16} + q^{17} + 6q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.