# Properties

 Label 6080.l Number of curves $2$ Conductor $6080$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("l1")

E.isogeny_class()

## Elliptic curves in class 6080.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6080.l1 6080s2 $$[0, 0, 0, -692, 6976]$$ $$8947094976/45125$$ $$184832000$$ $$[2]$$ $$2304$$ $$0.43300$$
6080.l2 6080s1 $$[0, 0, 0, -67, -24]$$ $$519718464/296875$$ $$19000000$$ $$[2]$$ $$1152$$ $$0.086424$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6080.2.a.l

sage: E.q_eigenform(10)

$$q + q^{5} - 2 q^{7} - 3 q^{9} - 4 q^{11} + 4 q^{13} + 6 q^{17} - q^{19} + O(q^{20})$$

## 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.