# Properties

 Label 22848.cw Number of curves $2$ Conductor $22848$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cw1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cw1 22848cq1 $$[0, 1, 0, -11989, -521101]$$ $$-11632923639808/318495051$$ $$-5218222915584$$ $$[]$$ $$55296$$ $$1.2215$$ $$\Gamma_0(N)$$-optimal
22848.cw2 22848cq2 $$[0, 1, 0, 53291, -2068237]$$ $$1021544365555712/705905647251$$ $$-11565558124560384$$ $$[]$$ $$165888$$ $$1.7708$$

## Rank

sage: E.rank()

The elliptic curves in class 22848.cw have rank $$0$$.

## Complex multiplication

The elliptic curves in class 22848.cw do not have complex multiplication.

## Modular form 22848.2.a.cw

sage: E.q_eigenform(10)

$$q + q^{3} + 3q^{5} - q^{7} + q^{9} - 3q^{11} + q^{13} + 3q^{15} + q^{17} + 5q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 