# Properties

 Label 11088bz Number of curves 4 Conductor 11088 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11088.n1")

sage: E.isogeny_class()

## Elliptic curves in class 11088bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.n4 11088bz1 [0, 0, 0, -92811, -3600326]  92160 $$\Gamma_0(N)$$-optimal
11088.n2 11088bz2 [0, 0, 0, -830091, 288510010] [2, 2] 184320
11088.n1 11088bz3 [0, 0, 0, -13248651, 18561179194]  368640
11088.n3 11088bz4 [0, 0, 0, -208011, 710902330]  368640

## Rank

sage: E.rank()

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

## Modular form 11088.2.a.n

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} + q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 