# Properties

 Label 3360.w Number of curves $2$ Conductor $3360$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.w1 3360l1 $$[0, 1, 0, -210, 900]$$ $$16079333824/2953125$$ $$189000000$$ $$$$ $$1152$$ $$0.30659$$ $$\Gamma_0(N)$$-optimal
3360.w2 3360l2 $$[0, 1, 0, 415, 5775]$$ $$1925134784/4465125$$ $$-18289152000$$ $$$$ $$2304$$ $$0.65316$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.w

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} + 2 q^{11} - 4 q^{13} + q^{15} - 2 q^{17} - 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 