# Properties

 Label 185130bf Number of curves 6 Conductor 185130 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("185130.dp1")

sage: E.isogeny_class()

## Elliptic curves in class 185130bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185130.dp4 185130bf1 [1, -1, 1, -7960613, 8647031517] [2] 5898240 $$\Gamma_0(N)$$-optimal
185130.dp3 185130bf2 [1, -1, 1, -8047733, 8448153981] [2, 2] 11796480
185130.dp5 185130bf3 [1, -1, 1, 4170847, 31824741237] [2] 23592960
185130.dp2 185130bf4 [1, -1, 1, -21660233, -27657641019] [2, 2] 23592960
185130.dp6 185130bf5 [1, -1, 1, 57020017, -182468900919] [2] 47185920
185130.dp1 185130bf6 [1, -1, 1, -318140483, -2183780611119] [2] 47185920

## Rank

sage: E.rank()

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

## Modular form 185130.2.a.dp

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.