# Properties

 Label 28900d Number of curves 4 Conductor 28900 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28900.b1")

sage: E.isogeny_class()

## Elliptic curves in class 28900d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28900.b3 28900d1 [0, 1, 0, -9633, 246988]  55296 $$\Gamma_0(N)$$-optimal
28900.b4 28900d2 [0, 1, 0, 26492, 1691988]  110592
28900.b1 28900d3 [0, 1, 0, -298633, -62899512]  165888
28900.b2 28900d4 [0, 1, 0, -262508, -78650012]  331776

## Rank

sage: E.rank()

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

## Modular form 28900.2.a.b

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 