# Properties

 Label 28900.f Number of curves 2 Conductor 28900 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28900.f1")

sage: E.isogeny_class()

## Elliptic curves in class 28900.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28900.f1 28900b1 [0, 0, 0, -202300, 35005125]  165888 $$\Gamma_0(N)$$-optimal
28900.f2 28900b2 [0, 0, 0, -166175, 47901750]  331776

## Rank

sage: E.rank()

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

## Modular form 28900.2.a.f

sage: E.q_eigenform(10)

$$q - 4q^{7} - 3q^{9} - 2q^{11} + 6q^{13} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 