# Properties

 Label 28611.g Number of curves 4 Conductor 28611 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28611.g1")

sage: E.isogeny_class()

## Elliptic curves in class 28611.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28611.g1 28611u4 [1, -1, 1, -381101, -90369790] [2] 245760
28611.g2 28611u2 [1, -1, 1, -29966, -619684] [2, 2] 122880
28611.g3 28611u1 [1, -1, 1, -16961, 847280] [2] 61440 $$\Gamma_0(N)$$-optimal
28611.g4 28611u3 [1, -1, 1, 113089, -4911334] [2] 245760

## Rank

sage: E.rank()

The elliptic curves in class 28611.g have rank $$1$$.

## Modular form 28611.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - 2q^{5} - 4q^{7} + 3q^{8} + 2q^{10} + q^{11} - 2q^{13} + 4q^{14} - q^{16} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.