# Properties

 Label 11088.j Number of curves 2 Conductor 11088 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11088.j1")

sage: E.isogeny_class()

## Elliptic curves in class 11088.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.j1 11088bb1 [0, 0, 0, -411, -1206]  4608 $$\Gamma_0(N)$$-optimal
11088.j2 11088bb2 [0, 0, 0, 1509, -9270]  9216

## Rank

sage: E.rank()

The elliptic curves in class 11088.j have rank $$1$$.

## Modular form 11088.2.a.j

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 