# Properties

 Label 28594f Number of curves 4 Conductor 28594 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28594.e1")

sage: E.isogeny_class()

## Elliptic curves in class 28594f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28594.e4 28594f1 [1, 1, 0, -2540, 29456] [2] 50400 $$\Gamma_0(N)$$-optimal
28594.e3 28594f2 [1, 1, 0, -36180, 2633192] [2] 100800
28594.e2 28594f3 [1, 1, 0, -86640, -9850612] [2] 151200
28594.e1 28594f4 [1, 1, 0, -95050, -7833894] [2] 302400

## Rank

sage: E.rank()

The elliptic curves in class 28594f have rank $$0$$.

## Modular form 28594.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - 4q^{7} - q^{8} + q^{9} - 6q^{11} + 2q^{12} + 2q^{13} + 4q^{14} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.