# Properties

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

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("28880.s1")

sage: E.isogeny_class()

## Elliptic curves in class 28880h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28880.s3 28880h1 [0, 0, 0, -722, 6859] [2] 13824 $$\Gamma_0(N)$$-optimal
28880.s2 28880h2 [0, 0, 0, -2527, -41154] [2, 2] 27648
28880.s4 28880h3 [0, 0, 0, 4693, -233206] [2] 55296
28880.s1 28880h4 [0, 0, 0, -38627, -2921934] [2] 55296

## Rank

sage: E.rank()

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

## Modular form 28880.2.a.s

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - 3q^{9} - 4q^{11} + 2q^{13} + 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.