# Properties

 Label 111012a Number of curves 2 Conductor 111012 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("111012.c1")

sage: E.isogeny_class()

## Elliptic curves in class 111012a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
111012.c2 111012a1 [0, -1, 0, 2243, -23330]  140448 $$\Gamma_0(N)$$-optimal
111012.c1 111012a2 [0, -1, 0, -10372, -189848]  280896

## Rank

sage: E.rank()

The elliptic curves in class 111012a have rank $$0$$.

## Modular form 111012.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - 2q^{7} + q^{9} - q^{11} - 2q^{13} - 2q^{15} - 4q^{17} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 