# Properties

 Label 450840u Number of curves $2$ Conductor $450840$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 450840u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.u1 450840u1 $$[0, -1, 0, -449567340, -3668785137900]$$ $$330999787611942608/200201625$$ $$6077820308479669152000$$ $$[2]$$ $$97763328$$ $$3.5022$$ $$\Gamma_0(N)$$-optimal
450840.u2 450840u2 $$[0, -1, 0, -446914320, -3714227125668]$$ $$-81293584906713092/2036310046875$$ $$-247277244772774687536000000$$ $$[2]$$ $$195526656$$ $$3.8488$$

## Rank

sage: E.rank()

The elliptic curves in class 450840u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 450840u do not have complex multiplication.

## Modular form 450840.2.a.u

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 2q^{7} + q^{9} + 4q^{11} - q^{13} - q^{15} + 8q^{19} + O(q^{20})$$

## 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.