# Properties

 Label 1088.l Number of curves 4 Conductor 1088 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1088.l1")

sage: E.isogeny_class()

## Elliptic curves in class 1088.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1088.l1 1088c4 [0, -1, 0, -7233, -161215] [2] 2304
1088.l2 1088c3 [0, -1, 0, -6593, -203839] [2] 1152
1088.l3 1088c2 [0, -1, 0, -2753, 56513] [2] 768
1088.l4 1088c1 [0, -1, 0, -193, 705] [2] 384 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1088.l have rank $$1$$.

## Modular form1088.2.a.l

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 LMFDB 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 LMFDB labels.