# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.v1 3360v2 $$[0, 1, 0, -14120, -650532]$$ $$608119035935048/826875$$ $$423360000$$ $$$$ $$3072$$ $$0.92955$$
3360.v2 3360v3 $$[0, 1, 0, -2240, 26520]$$ $$2428799546888/778248135$$ $$398463045120$$ $$$$ $$3072$$ $$0.92955$$
3360.v3 3360v1 $$[0, 1, 0, -890, -10200]$$ $$1219555693504/43758225$$ $$2800526400$$ $$[2, 2]$$ $$1536$$ $$0.58297$$ $$\Gamma_0(N)$$-optimal
3360.v4 3360v4 $$[0, 1, 0, 335, -34945]$$ $$1012048064/130203045$$ $$-533311672320$$ $$$$ $$3072$$ $$0.92955$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.v

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 