# Properties

 Label 3360.n Number of curves $4$ Conductor $3360$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.n1 3360i2 $$[0, 1, 0, -65576, -6485076]$$ $$60910917333827912/3255076125$$ $$1666598976000$$ $$$$ $$9216$$ $$1.4126$$
3360.n2 3360i3 $$[0, 1, 0, -21201, 1100799]$$ $$257307998572864/19456203375$$ $$79692609024000$$ $$$$ $$9216$$ $$1.4126$$
3360.n3 3360i1 $$[0, 1, 0, -4326, -90576]$$ $$139927692143296/27348890625$$ $$1750329000000$$ $$[2, 2]$$ $$4608$$ $$1.0660$$ $$\Gamma_0(N)$$-optimal
3360.n4 3360i4 $$[0, 1, 0, 8904, -524520]$$ $$152461584507448/322998046875$$ $$-165375000000000$$ $$$$ $$9216$$ $$1.4126$$

## Rank

sage: E.rank()

The elliptic curves in class 3360.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3360.n do not have complex multiplication.

## Modular form3360.2.a.n

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 