# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.ct1 22848bm2 $$[0, 1, 0, -24417, 1460223]$$ $$6141556990297/1019592$$ $$267279925248$$ $$[2]$$ $$36864$$ $$1.2006$$
22848.ct2 22848bm1 $$[0, 1, 0, -1377, 27135]$$ $$-1102302937/616896$$ $$-161715585024$$ $$[2]$$ $$18432$$ $$0.85405$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.ct

sage: E.q_eigenform(10)

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

## 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.