# Properties

 Label 6080.k Number of curves $4$ Conductor $6080$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("k1")

E.isogeny_class()

## Elliptic curves in class 6080.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6080.k1 6080c4 $$[0, 0, 0, -8108, 281008]$$ $$899466517764/95$$ $$6225920$$ $$[2]$$ $$4096$$ $$0.73189$$
6080.k2 6080c3 $$[0, 0, 0, -908, -3472]$$ $$1263284964/651605$$ $$42703585280$$ $$[2]$$ $$4096$$ $$0.73189$$
6080.k3 6080c2 $$[0, 0, 0, -508, 4368]$$ $$884901456/9025$$ $$147865600$$ $$[2, 2]$$ $$2048$$ $$0.38532$$
6080.k4 6080c1 $$[0, 0, 0, -8, 168]$$ $$-55296/11875$$ $$-12160000$$ $$[2]$$ $$1024$$ $$0.038746$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6080.k have rank $$0$$.

## Complex multiplication

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

## Modular form6080.2.a.k

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.