# Properties

 Label 22050.dt Number of curves $2$ Conductor $22050$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22050.dt1")

sage: E.isogeny_class()

## Elliptic curves in class 22050.dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.dt1 22050eg1 [1, -1, 1, -165605, -9872103]  258048 $$\Gamma_0(N)$$-optimal
22050.dt2 22050eg2 [1, -1, 1, 606145, -76242603]  516096

## Rank

sage: E.rank()

The elliptic curves in class 22050.dt have rank $$0$$.

## Modular form 22050.2.a.dt

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 2q^{11} + 2q^{13} + q^{16} + 4q^{17} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels. 