# Properties

 Label 6160.p Number of curves $2$ Conductor $6160$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6160.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6160.p1 6160o2 $$[0, -1, 0, -13560, -576400]$$ $$67324767141241/3368750000$$ $$13798400000000$$ $$$$ $$12288$$ $$1.2800$$
6160.p2 6160o1 $$[0, -1, 0, 520, -35728]$$ $$3789119879/135520000$$ $$-555089920000$$ $$$$ $$6144$$ $$0.93345$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6160.p have rank $$0$$.

## Complex multiplication

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

## Modular form6160.2.a.p

sage: E.q_eigenform(10)

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