# Properties

 Label 1110c Number of curves $4$ Conductor $1110$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1110.a1")

sage: E.isogeny_class()

## Elliptic curves in class 1110c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1110.a4 1110c1 [1, 1, 0, -1423388, -615252528]  49280 $$\Gamma_0(N)$$-optimal
1110.a2 1110c2 [1, 1, 0, -22394908, -40800879152] [2, 2] 98560
1110.a1 1110c3 [1, 1, 0, -358318108, -2610814913072]  197120
1110.a3 1110c4 [1, 1, 0, -22016028, -42247518768]  197120

## Rank

sage: E.rank()

The elliptic curves in class 1110c have rank $$1$$.

## Modular form1110.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} + 2q^{13} + 4q^{14} + q^{15} + q^{16} - 2q^{17} - q^{18} + 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 