# Properties

 Label 111090cx Number of curves 8 Conductor 111090 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("111090.da1")

sage: E.isogeny_class()

## Elliptic curves in class 111090cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
111090.da7 111090cx1 [1, 0, 0, 111079, -10728135] [2] 1441792 $$\Gamma_0(N)$$-optimal
111090.da6 111090cx2 [1, 0, 0, -566041, -96180679] [2, 2] 2883584
111090.da5 111090cx3 [1, 0, 0, -3993961, 3003344585] [2, 2] 5767168
111090.da4 111090cx4 [1, 0, 0, -7972041, -8661960279] [2] 5767168
111090.da8 111090cx5 [1, 0, 0, 671819, 9601690661] [2] 11534336
111090.da2 111090cx6 [1, 0, 0, -63506461, 194788327085] [2, 2] 11534336
111090.da3 111090cx7 [1, 0, 0, -63109711, 197342365535] [2] 23068672
111090.da1 111090cx8 [1, 0, 0, -1016103211, 12466711218635] [2] 23068672

## Rank

sage: E.rank()

The elliptic curves in class 111090cx have rank $$1$$.

## Modular form 111090.2.a.da

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - 2q^{13} + q^{14} - q^{15} + q^{16} - 2q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.