# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("11088.c1")

sage: E.isogeny_class()

## Elliptic curves in class 11088.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.c1 11088bi2 [0, 0, 0, -489, -7369] [] 6912
11088.c2 11088bi1 [0, 0, 0, 51, 191] [] 2304 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 11088.2.a.c

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 