# Properties

 Label 22848.cq Number of curves $2$ Conductor $22848$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cq1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.cq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cq1 22848cp2 $$[0, 1, 0, -1377, 18207]$$ $$2204605874/127449$$ $$16704995328$$ $$[2]$$ $$20480$$ $$0.71547$$
22848.cq2 22848cp1 $$[0, 1, 0, 63, 1215]$$ $$415292/9639$$ $$-631701504$$ $$[2]$$ $$10240$$ $$0.36890$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.cq

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} - q^{7} + q^{9} + 6q^{11} + 4q^{13} + 2q^{15} + q^{17} + 6q^{19} + O(q^{20})$$

## 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 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.