# Properties

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

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 6080.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6080.p1 6080p2 $$[0, 1, 0, -177921, 28826879]$$ $$-2376117230685121/342950$$ $$-89902284800$$ $$[]$$ $$13824$$ $$1.5109$$
6080.p2 6080p1 $$[0, 1, 0, -1921, 49279]$$ $$-2992209121/2375000$$ $$-622592000000$$ $$[]$$ $$4608$$ $$0.96155$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6080.2.a.p

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 