# Properties

 Label 11088i Number of curves 2 Conductor 11088 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11088.v1")

sage: E.isogeny_class()

## Elliptic curves in class 11088i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.v2 11088i1 [0, 0, 0, -75, -3638]  6144 $$\Gamma_0(N)$$-optimal
11088.v1 11088i2 [0, 0, 0, -4035, -97886]  12288

## Rank

sage: E.rank()

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

## Modular form 11088.2.a.v

sage: E.q_eigenform(10)

$$q - q^{7} - q^{11} + 2q^{13} + 8q^{17} + 6q^{19} + O(q^{20})$$

## 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. 