# Properties

 Label 28880y Number of curves 4 Conductor 28880 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28880.b1")

sage: E.isogeny_class()

## Elliptic curves in class 28880y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28880.b3 28880y1 [0, 1, 0, -481, 2634] [2] 13824 $$\Gamma_0(N)$$-optimal
28880.b4 28880y2 [0, 1, 0, 1324, 19240] [2] 27648
28880.b1 28880y3 [0, 1, 0, -14921, -706370] [2] 41472
28880.b2 28880y4 [0, 1, 0, -13116, -881816] [2] 82944

## Rank

sage: E.rank()

The elliptic curves in class 28880y have rank $$1$$.

## Modular form 28880.2.a.b

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} - 2q^{7} + q^{9} - 2q^{13} + 2q^{15} - 6q^{17} + O(q^{20})$$

## 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.