Properties

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

Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

Elliptic curves in class 3360g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.k3 3360g1 $$[0, -1, 0, -890, 10200]$$ $$1219555693504/43758225$$ $$2800526400$$ $$[2, 2]$$ $$1536$$ $$0.58297$$ $$\Gamma_0(N)$$-optimal
3360.k2 3360g2 $$[0, -1, 0, -2240, -26520]$$ $$2428799546888/778248135$$ $$398463045120$$ $$[2]$$ $$3072$$ $$0.92955$$
3360.k1 3360g3 $$[0, -1, 0, -14120, 650532]$$ $$608119035935048/826875$$ $$423360000$$ $$[4]$$ $$3072$$ $$0.92955$$
3360.k4 3360g4 $$[0, -1, 0, 335, 34945]$$ $$1012048064/130203045$$ $$-533311672320$$ $$[2]$$ $$3072$$ $$0.92955$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form3360.2.a.g

sage: E.q_eigenform(10)

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

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.