# Properties

 Label 28050c Number of curves 2 Conductor 28050 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28050.q1")

sage: E.isogeny_class()

## Elliptic curves in class 28050c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28050.q2 28050c1 [1, 1, 0, -22000, 544000]  129024 $$\Gamma_0(N)$$-optimal
28050.q1 28050c2 [1, 1, 0, -294000, 61200000]  258048

## Rank

sage: E.rank()

The elliptic curves in class 28050c have rank $$1$$.

## Modular form 28050.2.a.q

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 