# Properties

 Label 11088y Number of curves 4 Conductor 11088 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11088.o1")

sage: E.isogeny_class()

## Elliptic curves in class 11088y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.o4 11088y1 [0, 0, 0, 249, -59866]  16384 $$\Gamma_0(N)$$-optimal
11088.o3 11088y2 [0, 0, 0, -21531, -1188070] [2, 2] 32768
11088.o1 11088y3 [0, 0, 0, -342291, -77079886]  65536
11088.o2 11088y4 [0, 0, 0, -49251, 2498690]  65536

## Rank

sage: E.rank()

The elliptic curves in class 11088y have rank $$0$$.

## Modular form 11088.2.a.o

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} + q^{11} + 6q^{13} - 6q^{17} + O(q^{20})$$

## 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. 