# Properties

 Label 270480.ix Number of curves $2$ Conductor $270480$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 270480.ix

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.ix1 270480ix1 $$[0, 1, 0, -18440, 525300]$$ $$1439069689/579600$$ $$279303620198400$$ $$$$ $$884736$$ $$1.4699$$ $$\Gamma_0(N)$$-optimal
270480.ix2 270480ix2 $$[0, 1, 0, 59960, 3880820]$$ $$49471280711/41992020$$ $$-20235547283374080$$ $$$$ $$1769472$$ $$1.8165$$

## Rank

sage: E.rank()

The elliptic curves in class 270480.ix have rank $$0$$.

## Complex multiplication

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

## Modular form 270480.2.a.ix

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + 2q^{11} - 4q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 