# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("110.c1")

sage: E.isogeny_class()

## Elliptic curves in class 110.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110.c1 110b1 [1, 0, 0, -1, 1]  4 $$\Gamma_0(N)$$-optimal
110.c2 110b2 [1, 0, 0, 9, -25] [] 12

## Rank

sage: E.rank()

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

## Modular form110.2.a.c

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 