# Properties

 Label 4368.k Number of curves $4$ Conductor $4368$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 4368.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.k1 4368o3 $$[0, -1, 0, -6672, -207552]$$ $$8020417344913/187278$$ $$767090688$$ $$$$ $$4608$$ $$0.81712$$
4368.k2 4368o2 $$[0, -1, 0, -432, -2880]$$ $$2181825073/298116$$ $$1221083136$$ $$[2, 2]$$ $$2304$$ $$0.47055$$
4368.k3 4368o1 $$[0, -1, 0, -112, 448]$$ $$38272753/4368$$ $$17891328$$ $$$$ $$1152$$ $$0.12397$$ $$\Gamma_0(N)$$-optimal
4368.k4 4368o4 $$[0, -1, 0, 688, -16320]$$ $$8780064047/32388174$$ $$-132661960704$$ $$$$ $$4608$$ $$0.81712$$

## Rank

sage: E.rank()

The elliptic curves in class 4368.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4368.k do not have complex multiplication.

## Modular form4368.2.a.k

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 