# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 8280.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.s1 8280r1 $$[0, 0, 0, -162, -459]$$ $$1492992/575$$ $$181083600$$ $$$$ $$2688$$ $$0.28359$$ $$\Gamma_0(N)$$-optimal
8280.s2 8280r2 $$[0, 0, 0, 513, -3294]$$ $$2963088/2645$$ $$-13327752960$$ $$$$ $$5376$$ $$0.63017$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8280.2.a.s

sage: E.q_eigenform(10)

$$q + q^{5} + 2 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})$$

## 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. 