# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 6080.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6080.t1 6080b1 $$[0, -1, 0, -141, 605]$$ $$304900096/45125$$ $$46208000$$ $$$$ $$1536$$ $$0.19535$$ $$\Gamma_0(N)$$-optimal
6080.t2 6080b2 $$[0, -1, 0, 239, 2961]$$ $$91765424/296875$$ $$-4864000000$$ $$$$ $$3072$$ $$0.54193$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6080.2.a.t

sage: E.q_eigenform(10)

$$q + 2 q^{3} - q^{5} + q^{9} + 4 q^{11} - 4 q^{13} - 2 q^{15} - 2 q^{17} - q^{19} + O(q^{20})$$

## 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. 