# Properties

 Label 22848.cm Number of curves $4$ Conductor $22848$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cm1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cm1 22848co4 $$[0, 1, 0, -2177, 34815]$$ $$17418812548/1753941$$ $$114946277376$$ $$$$ $$20480$$ $$0.85845$$
22848.cm2 22848co2 $$[0, 1, 0, -497, -3825]$$ $$830321872/127449$$ $$2088124416$$ $$[2, 2]$$ $$10240$$ $$0.51187$$
22848.cm3 22848co1 $$[0, 1, 0, -477, -4173]$$ $$11745974272/357$$ $$365568$$ $$$$ $$5120$$ $$0.16530$$ $$\Gamma_0(N)$$-optimal
22848.cm4 22848co3 $$[0, 1, 0, 863, -19873]$$ $$1083360092/3306177$$ $$-216673615872$$ $$$$ $$20480$$ $$0.85845$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.cm

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 