# Properties

 Label 41280k Number of curves $2$ Conductor $41280$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 41280k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41280.g2 41280k1 $$[0, -1, 0, -2401, 31201]$$ $$5841725401/1857600$$ $$486958694400$$ $$$$ $$55296$$ $$0.94645$$ $$\Gamma_0(N)$$-optimal
41280.g1 41280k2 $$[0, -1, 0, -15201, -693279]$$ $$1481933914201/53916840$$ $$14133976104960$$ $$$$ $$110592$$ $$1.2930$$

## Rank

sage: E.rank()

The elliptic curves in class 41280k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 41280k do not have complex multiplication.

## Modular form 41280.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 2q^{7} + q^{9} + 2q^{11} + 2q^{13} + q^{15} - 4q^{17} + 6q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 