# Properties

 Label 19890.n Number of curves 8 Conductor 19890 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19890.n1")
sage: E.isogeny_class()

## Elliptic curves in class 19890.n

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
19890.n1 19890r7 [1, -1, 0, -59319000054, 5560834936210128] 6 26542080
19890.n2 19890r6 [1, -1, 0, -3707437554, 86888738522628] 12 13271040
19890.n3 19890r8 [1, -1, 0, -3700714734, 87219545637240] 6 26542080
19890.n4 19890r4 [1, -1, 0, -732359394, 7627624175700] 2 8847360
19890.n5 19890r3 [1, -1, 0, -232135074, 1352508703380] 6 6635520
19890.n6 19890r2 [1, -1, 0, -50015394, 95774634900] 4 4423680
19890.n7 19890r1 [1, -1, 0, -18865314, -30364499052] 2 2211840 $$\Gamma_0(N)$$-optimal
19890.n8 19890r5 [1, -1, 0, 133927326, 636455866068] 2 8847360

## Rank

sage: E.rank()

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

## Modular form 19890.2.a.n

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} + q^{5} - 4q^{7} - q^{8} - q^{10} + q^{13} + 4q^{14} + q^{16} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.