# Properties

 Label 6080.f Number of curves $2$ Conductor $6080$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6080.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6080.f1 6080j1 $$[0, 1, 0, -3685, 79083]$$ $$5405726654464/407253125$$ $$417027200000$$ $$$$ $$7680$$ $$0.97495$$ $$\Gamma_0(N)$$-optimal
6080.f2 6080j2 $$[0, 1, 0, 3535, 357775]$$ $$298091207216/3525390625$$ $$-57760000000000$$ $$$$ $$15360$$ $$1.3215$$

## Rank

sage: E.rank()

The elliptic curves in class 6080.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 6080.f do not have complex multiplication.

## Modular form6080.2.a.f

sage: E.q_eigenform(10)

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

## 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. 