# Properties

 Label 270480is Number of curves $4$ Conductor $270480$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("is1")

sage: E.isogeny_class()

## Elliptic curves in class 270480is

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270480.is3 270480is1 $$[0, 1, 0, -99664840, 410132431988]$$ $$-227196402372228188089/19338934824115200$$ $$-9319245181429060259020800$$ $$[2]$$ $$53084160$$ $$3.5360$$ $$\Gamma_0(N)$$-optimal
270480.is2 270480is2 $$[0, 1, 0, -1625893320, 25233322922100]$$ $$986396822567235411402169/6336721794060000$$ $$3053604791702998794240000$$ $$[2]$$ $$106168320$$ $$3.8826$$
270480.is4 270480is3 $$[0, 1, 0, 590870600, 15362652500]$$ $$47342661265381757089751/27397579603968000000$$ $$-13202627964220339126272000000$$ $$[2]$$ $$159252480$$ $$4.0853$$
270480.is1 270480is4 $$[0, 1, 0, -2363492280, 120537971028]$$ $$3029968325354577848895529/1753440696000000000000$$ $$844966070041411584000000000000$$ $$[2]$$ $$318504960$$ $$4.4319$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 270480.2.a.is

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + 4q^{13} + q^{15} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.