# Properties

 Label 32200u Number of curves $2$ Conductor $32200$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 32200u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32200.f2 32200u1 $$[0, 1, 0, -708, 9088]$$ $$-9826000/3703$$ $$-14812000000$$ $$$$ $$23040$$ $$0.66139$$ $$\Gamma_0(N)$$-optimal
32200.f1 32200u2 $$[0, 1, 0, -12208, 515088]$$ $$12576878500/1127$$ $$18032000000$$ $$$$ $$46080$$ $$1.0080$$

## Rank

sage: E.rank()

The elliptic curves in class 32200u have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32200u do not have complex multiplication.

## Modular form 32200.2.a.u

sage: E.q_eigenform(10)

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