# Properties

 Label 22848.h Number of curves $4$ Conductor $22848$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 22848.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.h1 22848b4 $$[0, -1, 0, -5089, -138047]$$ $$444893916104/9639$$ $$315850752$$ $$$$ $$14336$$ $$0.74729$$
22848.h2 22848b2 $$[0, -1, 0, -329, -1911]$$ $$964430272/127449$$ $$522031104$$ $$[2, 2]$$ $$7168$$ $$0.40071$$
22848.h3 22848b1 $$[0, -1, 0, -84, 294]$$ $$1036433728/122451$$ $$7836864$$ $$$$ $$3584$$ $$0.054141$$ $$\Gamma_0(N)$$-optimal
22848.h4 22848b3 $$[0, -1, 0, 511, -10815]$$ $$449455096/1753941$$ $$-57473138688$$ $$$$ $$14336$$ $$0.74729$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 22848.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{13} + 2q^{15} - q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 