# Properties

 Label 334620.ch Number of curves $4$ Conductor $334620$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ch1")

sage: E.isogeny_class()

## Elliptic curves in class 334620.ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
334620.ch1 334620ch4 $$[0, 0, 0, -10799607, 13660291294]$$ $$154639330142416/33275$$ $$29974066853702400$$ $$$$ $$11197440$$ $$2.5462$$
334620.ch2 334620ch3 $$[0, 0, 0, -677352, 211863301]$$ $$610462990336/8857805$$ $$498693537278473680$$ $$$$ $$5598720$$ $$2.1997$$
334620.ch3 334620ch2 $$[0, 0, 0, -152607, 12966694]$$ $$436334416/171875$$ $$154824725484000000$$ $$$$ $$3732480$$ $$1.9969$$
334620.ch4 334620ch1 $$[0, 0, 0, -68952, -6826079]$$ $$643956736/15125$$ $$851535990162000$$ $$$$ $$1866240$$ $$1.6504$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 334620.ch have rank $$0$$.

## Complex multiplication

The elliptic curves in class 334620.ch do not have complex multiplication.

## Modular form 334620.2.a.ch

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - q^{11} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 