# Properties

 Label 270480ch Number of curves $2$ Conductor $270480$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 270480ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.ch1 270480ch1 $$[0, -1, 0, -192096, 31000320]$$ $$1626794704081/83462400$$ $$40219721308569600$$ $$$$ $$3538944$$ $$1.9440$$ $$\Gamma_0(N)$$-optimal
270480.ch2 270480ch2 $$[0, -1, 0, 121504, 122069760]$$ $$411664745519/13605414480$$ $$-6556317319813201920$$ $$$$ $$7077888$$ $$2.2906$$

## Rank

sage: E.rank()

The elliptic curves in class 270480ch have rank $$1$$.

## Complex multiplication

The elliptic curves in class 270480ch do not have complex multiplication.

## Modular form 270480.2.a.ch

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{9} + 6q^{11} + q^{15} - 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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 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. 