# Properties

 Label 110c Number of curves 2 Conductor 110 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("110.a1")

sage: E.isogeny_class()

## Elliptic curves in class 110c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110.a1 110c1 [1, 0, 1, -89, 316]  28 $$\Gamma_0(N)$$-optimal
110.a2 110c2 [1, 0, 1, 296, 1702] [] 84

## Rank

sage: E.rank()

The elliptic curves in class 110c have rank $$0$$.

## Modular form110.2.a.a

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 