# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("by1")

sage: E.isogeny_class()

## Elliptic curves in class 22848by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.g2 22848by1 $$[0, -1, 0, 5831, -5831]$$ $$5352028359488/3098832471$$ $$-12692817801216$$ $$$$ $$46080$$ $$1.2038$$ $$\Gamma_0(N)$$-optimal
22848.g1 22848by2 $$[0, -1, 0, -23329, -23327]$$ $$42852953779784/24786408969$$ $$812201049096192$$ $$$$ $$92160$$ $$1.5504$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.by

sage: E.q_eigenform(10)

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