# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("11088.a1")

sage: E.isogeny_class()

## Elliptic curves in class 11088.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.a1 11088bc2 [0, 0, 0, -5967, 152010]  23040
11088.a2 11088bc1 [0, 0, 0, 648, 13095]  11520 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 11088.2.a.a

sage: E.q_eigenform(10)

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

## 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. 