# Properties

 Label 28900i Number of curves 2 Conductor 28900 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28900.c1")

sage: E.isogeny_class()

## Elliptic curves in class 28900i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28900.c2 28900i1 [0, -1, 0, 84292, -2530088] [] 103680 $$\Gamma_0(N)$$-optimal
28900.c1 28900i2 [0, -1, 0, -1360708, -632550088] [] 311040

## Rank

sage: E.rank()

The elliptic curves in class 28900i have rank $$1$$.

## Modular form 28900.2.a.c

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. 