# Properties

 Label 1088i Number of curves 4 Conductor 1088 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1088.d1")

sage: E.isogeny_class()

## Elliptic curves in class 1088i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1088.d4 1088i1 [0, 1, 0, -193, -705]  384 $$\Gamma_0(N)$$-optimal
1088.d3 1088i2 [0, 1, 0, -2753, -56513]  768
1088.d2 1088i3 [0, 1, 0, -6593, 203839]  1152
1088.d1 1088i4 [0, 1, 0, -7233, 161215]  2304

## Rank

sage: E.rank()

The elliptic curves in class 1088i have rank $$0$$.

## Modular form1088.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{3} + 4q^{7} + q^{9} + 6q^{11} - 2q^{13} - q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 