# Properties

 Label 22848.k Number of curves $2$ Conductor $22848$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.k1 22848cc1 $$[0, -1, 0, -1349, 19509]$$ $$265327034368/297381$$ $$304518144$$ $$$$ $$11520$$ $$0.54191$$ $$\Gamma_0(N)$$-optimal
22848.k2 22848cc2 $$[0, -1, 0, -1009, 29233]$$ $$-6940769488/18000297$$ $$-294916866048$$ $$$$ $$23040$$ $$0.88849$$

## Rank

sage: E.rank()

The elliptic curves in class 22848.k have rank $$1$$.

## Complex multiplication

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

## Modular form 22848.2.a.k

sage: E.q_eigenform(10)

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