# Properties

 Label 3330.i Number of curves $2$ Conductor $3330$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 3330.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.i1 3330c2 $$[1, -1, 0, -5739, -165907]$$ $$1062144635427/54760$$ $$1077841080$$ $$$$ $$3456$$ $$0.80252$$
3330.i2 3330c1 $$[1, -1, 0, -339, -2827]$$ $$-219256227/59200$$ $$-1165233600$$ $$$$ $$1728$$ $$0.45594$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3330.2.a.i

sage: E.q_eigenform(10)

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