# Properties

 Label 705600.ix Number of curves $4$ Conductor $705600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ix1")

sage: E.isogeny_class()

## Elliptic curves in class 705600.ix

sage: E.isogeny_class().curves

LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.ix1 $$[0, 0, 0, -4500846014700, 3675270815038186000]$$ $$229625675762164624948320008/9568125$$ $$420157934844480000000000$$ $$[2]$$ $$7927234560$$ $$5.4335$$
705600.ix2 $$[0, 0, 0, -281302889700, 57426100576936000]$$ $$448487713888272974160064/91549016015625$$ $$502515455041730025000000000000$$ $$[2, 2]$$ $$3963617280$$ $$5.0870$$
705600.ix3 $$[0, 0, 0, -280338422700, 57839426767654000]$$ $$-55486311952875723077768/801237030029296875$$ $$-35184123938392734375000000000000000$$ $$[2]$$ $$7927234560$$ $$5.4335$$
705600.ix4 $$[0, 0, 0, -17641723575, 890818691749000]$$ $$7079962908642659949376/100085966990454375$$ $$8583985155305315771229375000000$$ $$[2]$$ $$1981808640$$ $$4.7404$$

## Rank

sage: E.rank()

The elliptic curves in class 705600.ix have rank $$0$$.

## Complex multiplication

The elliptic curves in class 705600.ix do not have complex multiplication.

## Modular form 705600.2.a.ix

sage: E.q_eigenform(10)

$$q - 4q^{11} + 6q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.