# Properties

 Label 4018.s Number of curves $2$ Conductor $4018$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 4018.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4018.s1 4018s2 [1, -1, 1, -470954322, 3933954127513] [] 1185408
4018.s2 4018s1 [1, -1, 1, -948282, -326942087] [] 169344 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4018.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4018.s do not have complex multiplication.

## Modular form4018.2.a.s

sage: E.q_eigenform(10)

$$q + q^{2} + 3q^{3} + q^{4} + q^{5} + 3q^{6} + q^{8} + 6q^{9} + q^{10} - 2q^{11} + 3q^{12} + 3q^{15} + q^{16} + 3q^{17} + 6q^{18} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.