# Properties

 Label 19890.m Number of curves 4 Conductor 19890 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19890.m1")

sage: E.isogeny_class()

## Elliptic curves in class 19890.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19890.m1 19890l3 [1, -1, 0, -689580, -219859304]  368640
19890.m2 19890l4 [1, -1, 0, -577980, 168395656]  368640
19890.m3 19890l2 [1, -1, 0, -57780, -877424] [2, 2] 184320
19890.m4 19890l1 [1, -1, 0, 14220, -114224]  92160 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 19890.m have rank $$0$$.

## Modular form 19890.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + 4q^{7} - q^{8} + q^{10} + 4q^{11} + q^{13} - 4q^{14} + q^{16} + q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 