# Properties

 Label 4018.i Number of curves 2 Conductor 4018 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4018.i1")

sage: E.isogeny_class()

## Elliptic curves in class 4018.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4018.i1 4018g2 [1, 1, 0, -33664887, -75117062635]  783360
4018.i2 4018g1 [1, 1, 0, -1552247, -1803905515]  391680 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4018.i have rank $$1$$.

## Modular form4018.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 4q^{5} - 2q^{6} - q^{8} + q^{9} + 4q^{10} + 4q^{11} + 2q^{12} - 4q^{13} - 8q^{15} + q^{16} + 2q^{17} - q^{18} + 6q^{19} + O(q^{20})$$

## 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. 