# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 480.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
480.d1 480b2 $$[0, -1, 0, -160, -728]$$ $$890277128/15$$ $$7680$$ $$$$ $$64$$ $$-0.12420$$
480.d2 480b3 $$[0, -1, 0, -40, 100]$$ $$14172488/1875$$ $$960000$$ $$$$ $$64$$ $$-0.12420$$
480.d3 480b1 $$[0, -1, 0, -10, -8]$$ $$1906624/225$$ $$14400$$ $$[2, 2]$$ $$32$$ $$-0.47077$$ $$\Gamma_0(N)$$-optimal
480.d4 480b4 $$[0, -1, 0, 15, -63]$$ $$85184/405$$ $$-1658880$$ $$$$ $$64$$ $$-0.12420$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form480.2.a.d

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 