# Properties

 Label 22848h Number of curves $4$ Conductor $22848$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 22848h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.bb4 22848h1 $$[0, -1, 0, -2826577, 1847044945]$$ $$-152435594466395827792/1646846627220711$$ $$-26981935140384129024$$ $$[2]$$ $$552960$$ $$2.5444$$ $$\Gamma_0(N)$$-optimal
22848.bb3 22848h2 $$[0, -1, 0, -45341857, 117531121825]$$ $$157304700372188331121828/18069292138401$$ $$1184189129582247936$$ $$[2, 2]$$ $$1105920$$ $$2.8910$$
22848.bb2 22848h3 $$[0, -1, 0, -45458497, 116896156993]$$ $$79260902459030376659234/842751810121431609$$ $$110461165256236283854848$$ $$[2]$$ $$2211840$$ $$3.2376$$
22848.bb1 22848h4 $$[0, -1, 0, -725469697, 7521266762497]$$ $$322159999717985454060440834/4250799$$ $$557160726528$$ $$[4]$$ $$2211840$$ $$3.2376$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{5} - q^{7} + q^{9} - 2 q^{13} - 2 q^{15} + q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.