# Properties

 Label 28050dg Number of curves $2$ Conductor $28050$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dg1")

sage: E.isogeny_class()

## Elliptic curves in class 28050dg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28050.dn2 28050dg1 [1, 0, 0, 662, 5792] [2] 24576 $$\Gamma_0(N)$$-optimal
28050.dn1 28050dg2 [1, 0, 0, -3588, 52542] [2] 49152

## Rank

sage: E.rank()

The elliptic curves in class 28050dg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 28050dg do not have complex multiplication.

## Modular form 28050.2.a.dg

sage: E.q_eigenform(10)

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

## 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.