# Properties

 Label 6160.a Number of curves $2$ Conductor $6160$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 6160.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6160.a1 6160h2 $$[0, 1, 0, -1176, 15124]$$ $$43949604889/42350$$ $$173465600$$ $$$$ $$3072$$ $$0.50213$$
6160.a2 6160h1 $$[0, 1, 0, -56, 340]$$ $$-4826809/10780$$ $$-44154880$$ $$$$ $$1536$$ $$0.15556$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6160.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 6160.a do not have complex multiplication.

## Modular form6160.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + 2q^{13} + 2q^{15} + 2q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 