# Properties

 Label 155526h Number of curves $6$ Conductor $155526$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("155526.cp1")

sage: E.isogeny_class()

## Elliptic curves in class 155526h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
155526.cp5 155526h1 [1, 0, 0, 3265506, 4652171460] [2] 12976128 $$\Gamma_0(N)$$-optimal
155526.cp4 155526h2 [1, 0, 0, -29913374, 53882993604] [2, 2] 25952256
155526.cp2 155526h3 [1, 0, 0, -459165134, 3786913849620] [2] 51904512
155526.cp3 155526h4 [1, 0, 0, -131523694, -528242529676] [2, 2] 51904512
155526.cp6 155526h5 [1, 0, 0, 162420446, -2554517064352] [2] 103809024
155526.cp1 155526h6 [1, 0, 0, -2051232954, -35757595043640] [2] 103809024

## Rank

sage: E.rank()

The elliptic curves in class 155526h have rank $$1$$.

## Modular form 155526.2.a.cp

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.