# Properties

 Label 19110cn Number of curves $6$ Conductor $19110$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19110.cv1")

sage: E.isogeny_class()

## Elliptic curves in class 19110cn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19110.cv6 19110cn1 [1, 0, 0, 734, -3004]  24576 $$\Gamma_0(N)$$-optimal
19110.cv5 19110cn2 [1, 0, 0, -3186, -25740] [2, 2] 49152
19110.cv2 19110cn3 [1, 0, 0, -41406, -3243864]  98304
19110.cv3 19110cn4 [1, 0, 0, -27686, 1752960] [2, 2] 98304
19110.cv1 19110cn5 [1, 0, 0, -441736, 112966790]  196608
19110.cv4 19110cn6 [1, 0, 0, -5636, 4473930]  196608

## Rank

sage: E.rank()

The elliptic curves in class 19110cn have rank $$0$$.

## Modular form 19110.2.a.cv

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 