# Properties

 Label 8280.f Number of curves $2$ Conductor $8280$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 8280.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.f1 8280g2 $$[0, 0, 0, -4668483, -3882494882]$$ $$7536914291382802562/17961229575$$ $$26815972065638400$$ $$$$ $$168960$$ $$2.3937$$
8280.f2 8280g1 $$[0, 0, 0, -288363, -62154218]$$ $$-3552342505518244/179863605135$$ $$-134267461778856960$$ $$$$ $$84480$$ $$2.0471$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8280.f have rank $$1$$.

## Complex multiplication

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

## Modular form8280.2.a.f

sage: E.q_eigenform(10)

$$q - q^{5} - 2 q^{11} - 6 q^{17} + 8 q^{19} + O(q^{20})$$

## 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. 