# Properties

 Label 22050.c Number of curves $4$ Conductor $22050$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22050.c1")

sage: E.isogeny_class()

## Elliptic curves in class 22050.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.c1 22050k4 [1, -1, 0, -266667, 13921991]  414720
22050.c2 22050k2 [1, -1, 0, -156417, -23771259]  138240
22050.c3 22050k1 [1, -1, 0, -9417, -398259]  69120 $$\Gamma_0(N)$$-optimal
22050.c4 22050k3 [1, -1, 0, 64083, 1684241]  207360

## Rank

sage: E.rank()

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

## Modular form 22050.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 6q^{11} - 4q^{13} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 