# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.bt1 22848x2 $$[0, 1, 0, -3531169, 2552810687]$$ $$18575453384550358633/352517816448$$ $$92410430474944512$$ $$$$ $$516096$$ $$2.3791$$
22848.bt2 22848x1 $$[0, 1, 0, -213409, 42593471]$$ $$-4100379159705193/626805817344$$ $$-164313384181825536$$ $$$$ $$258048$$ $$2.0325$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.bt

sage: E.q_eigenform(10)

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