# Properties

 Label 11088bj Number of curves 3 Conductor 11088 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11088.b1")

sage: E.isogeny_class()

## Elliptic curves in class 11088bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.b1 11088bj1 [0, 0, 0, -12864, 561584] [] 14400 $$\Gamma_0(N)$$-optimal
11088.b2 11088bj2 [0, 0, 0, -7104, 1065584] [] 43200
11088.b3 11088bj3 [0, 0, 0, 63456, -27581776] [] 129600

## Rank

sage: E.rank()

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

## Modular form 11088.2.a.b

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 