# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4018.f1")
sage: E.isogeny_class()

## Elliptic curves in class 4018.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4018.f1 4018c2 [1, 1, 0, -114391, 14839637] 1 17280
4018.f2 4018c1 [1, 1, 0, -3896, -69152] 1 5760 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form4018.2.a.f

sage: E.q_eigenform(10)
$$q - q^{2} - q^{3} + q^{4} + 3q^{5} + q^{6} - q^{8} - 2q^{9} - 3q^{10} - q^{12} - 2q^{13} - 3q^{15} + q^{16} + 3q^{17} + 2q^{18} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.