# Properties

 Label 3360.m Number of curves $2$ Conductor $3360$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.m1 3360r1 $$[0, -1, 0, -1370, -19068]$$ $$4446542056384/25725$$ $$1646400$$ $$[2]$$ $$1920$$ $$0.38319$$ $$\Gamma_0(N)$$-optimal
3360.m2 3360r2 $$[0, -1, 0, -1345, -19823]$$ $$-65743598656/5294205$$ $$-21685063680$$ $$[2]$$ $$3840$$ $$0.72976$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.m

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} + 6q^{11} + 4q^{13} - q^{15} + 6q^{17} + 6q^{19} + O(q^{20})$$

## 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.