# Properties

 Label 184041j Number of curves $2$ Conductor $184041$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 184041j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
184041.k2 184041j1 [1, -1, 1, -45662, 3767118] [] 336960 $$\Gamma_0(N)$$-optimal
184041.k1 184041j2 [1, -1, 1, -463937, -475341798] [] 3706560

## Rank

sage: E.rank()

The elliptic curves in class 184041j have rank $$1$$.

## Complex multiplication

The elliptic curves in class 184041j do not have complex multiplication.

## Modular form 184041.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + q^{5} - 2q^{7} + 3q^{8} - q^{10} + 2q^{14} - q^{16} - 5q^{17} + 6q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.