# Properties

 Label 6160.e Number of curves $4$ Conductor $6160$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 6160.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6160.e1 6160j4 $$[0, 0, 0, -334547, 74478994]$$ $$1010962818911303721/57392720$$ $$235080581120$$ $$$$ $$24576$$ $$1.6485$$
6160.e2 6160j3 $$[0, 0, 0, -35027, -595054]$$ $$1160306142246441/634128110000$$ $$2597388738560000$$ $$$$ $$24576$$ $$1.6485$$
6160.e3 6160j2 $$[0, 0, 0, -20947, 1159314]$$ $$248158561089321/1859334400$$ $$7615833702400$$ $$[2, 2]$$ $$12288$$ $$1.3020$$
6160.e4 6160j1 $$[0, 0, 0, -467, 41106]$$ $$-2749884201/176619520$$ $$-723433553920$$ $$$$ $$6144$$ $$0.95539$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6160.2.a.e

sage: E.q_eigenform(10)

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