# Properties

 Label 18150.m Number of curves 4 Conductor 18150 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18150.m1")

sage: E.isogeny_class()

## Elliptic curves in class 18150.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18150.m1 18150i3 [1, 1, 0, -243575, 45991125] [2] 207360
18150.m2 18150i4 [1, 1, 0, -122575, 91850125] [2] 414720
18150.m3 18150i1 [1, 1, 0, -16700, -790500] [2] 69120 $$\Gamma_0(N)$$-optimal
18150.m4 18150i2 [1, 1, 0, 13550, -3301250] [2] 138240

## Rank

sage: E.rank()

The elliptic curves in class 18150.m have rank $$0$$.

## Modular form 18150.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} + 2q^{7} - q^{8} + q^{9} - q^{12} - 4q^{13} - 2q^{14} + q^{16} - 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.