# Properties

 Label 3330.u Number of curves $2$ Conductor $3330$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3330.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.u1 3330ba2 $$[1, -1, 1, -63797, 6225869]$$ $$-39390416456458249/56832000000$$ $$-41430528000000$$ $$[3]$$ $$17280$$ $$1.5153$$
3330.u2 3330ba1 $$[1, -1, 1, 1138, 40061]$$ $$223759095911/1094104800$$ $$-797602399200$$ $$[]$$ $$5760$$ $$0.96602$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3330.u have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3330.u do not have complex multiplication.

## Modular form3330.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - 3q^{11} - 7q^{13} - q^{14} + q^{16} + 3q^{17} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.