# Properties

 Label 3360n Number of curves $4$ Conductor $3360$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3360n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.e3 3360n1 $$[0, -1, 0, -166, 616]$$ $$7952095936/2480625$$ $$158760000$$ $$[2, 2]$$ $$1024$$ $$0.27790$$ $$\Gamma_0(N)$$-optimal
3360.e2 3360n2 $$[0, -1, 0, -1041, -12159]$$ $$30488290624/1148175$$ $$4702924800$$ $$[2]$$ $$2048$$ $$0.62447$$
3360.e1 3360n3 $$[0, -1, 0, -2416, 46516]$$ $$3047363673992/540225$$ $$276595200$$ $$[4]$$ $$2048$$ $$0.62447$$
3360.e4 3360n4 $$[0, -1, 0, 464, 3640]$$ $$21531355768/24609375$$ $$-12600000000$$ $$[2]$$ $$2048$$ $$0.62447$$

## Rank

sage: E.rank()

The elliptic curves in class 3360n have rank $$1$$.

## Complex multiplication

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

## Modular form3360.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + 2q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.