# Properties

 Label 4368.u Number of curves $2$ Conductor $4368$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("u1")

E.isogeny_class()

## Elliptic curves in class 4368.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.u1 4368x2 $$[0, 1, 0, -6228, -191160]$$ $$104375673106000/69854967$$ $$17882871552$$ $$$$ $$3840$$ $$0.90583$$
4368.u2 4368x1 $$[0, 1, 0, -313, -4246]$$ $$-212629504000/340075827$$ $$-5441213232$$ $$$$ $$1920$$ $$0.55926$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4368.2.a.u

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 