# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bz1")

sage: E.isogeny_class()

## Elliptic curves in class 22848.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.bz1 22848ct2 $$[0, 1, 0, -1073889, -425939553]$$ $$1044942448578893426/7759962920241$$ $$1017113859881828352$$ $$$$ $$540672$$ $$2.2859$$
22848.bz2 22848ct1 $$[0, 1, 0, -24129, -15063489]$$ $$-23707171994692/1480419781911$$ $$-97020790827319296$$ $$$$ $$270336$$ $$1.9393$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.bz

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{7} + q^{9} + 6q^{11} - 4q^{13} - 2q^{15} - q^{17} + 2q^{19} + O(q^{20})$$ ## 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. 