# Properties

 Label 480.a Number of curves $4$ Conductor $480$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 480.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
480.a1 480e3 $$[0, -1, 0, -3601, 84385]$$ $$1261112198464/675$$ $$2764800$$ $$$$ $$384$$ $$0.56564$$
480.a2 480e2 $$[0, -1, 0, -496, -2204]$$ $$26410345352/10546875$$ $$5400000000$$ $$$$ $$384$$ $$0.56564$$
480.a3 480e1 $$[0, -1, 0, -226, 1360]$$ $$20034997696/455625$$ $$29160000$$ $$[2, 2]$$ $$192$$ $$0.21907$$ $$\Gamma_0(N)$$-optimal
480.a4 480e4 $$[0, -1, 0, 24, 3960]$$ $$2863288/13286025$$ $$-6802444800$$ $$$$ $$384$$ $$0.56564$$

## Rank

sage: E.rank()

The elliptic curves in class 480.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 480.a do not have complex multiplication.

## Modular form480.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 4q^{7} + q^{9} + 4q^{11} + 6q^{13} + q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 