# Properties

 Label 28900c Number of curves 2 Conductor 28900 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28900.k1")

sage: E.isogeny_class()

## Elliptic curves in class 28900c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28900.k2 28900c1 [0, 1, 0, 3372, -18892] [] 20736 $$\Gamma_0(N)$$-optimal
28900.k1 28900c2 [0, 1, 0, -54428, -5082172] [] 62208

## Rank

sage: E.rank()

The elliptic curves in class 28900c have rank $$0$$.

## Modular form 28900.2.a.k

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} - 2q^{9} + q^{13} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.