# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.i1 22848i2 $$[0, -1, 0, -89, 249]$$ $$19248832/6069$$ $$24858624$$ $$$$ $$4608$$ $$0.12311$$
22848.i2 22848i1 $$[0, -1, 0, 16, 18]$$ $$6644672/7497$$ $$-479808$$ $$$$ $$2304$$ $$-0.22346$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.i

sage: E.q_eigenform(10)

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