# Properties

 Label 8280.w Number of curves $2$ Conductor $8280$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 8280.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.w1 8280w2 $$[0, 0, 0, -7707, -237994]$$ $$33909572018/3234375$$ $$4828896000000$$ $$$$ $$21504$$ $$1.1716$$
8280.w2 8280w1 $$[0, 0, 0, 573, -17746]$$ $$27871484/198375$$ $$-148086144000$$ $$$$ $$10752$$ $$0.82504$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8280.w have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8280.w do not have complex multiplication.

## Modular form8280.2.a.w

sage: E.q_eigenform(10)

$$q + q^{5} + 4 q^{7} + 6 q^{11} - 4 q^{13} - 2 q^{17} + O(q^{20})$$

## 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. 