# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 3360.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.g1 3360f2 $$[0, -1, 0, -84000, -9342648]$$ $$128025588102048008/7875$$ $$4032000$$ $$$$ $$6144$$ $$1.1760$$
3360.g2 3360f3 $$[0, -1, 0, -5880, -107100]$$ $$43919722445768/15380859375$$ $$7875000000000$$ $$$$ $$6144$$ $$1.1760$$
3360.g3 3360f1 $$[0, -1, 0, -5250, -144648]$$ $$250094631024064/62015625$$ $$3969000000$$ $$[2, 2]$$ $$3072$$ $$0.82939$$ $$\Gamma_0(N)$$-optimal
3360.g4 3360f4 $$[0, -1, 0, -4625, -181023]$$ $$-2671731885376/1969120125$$ $$-8065516032000$$ $$$$ $$6144$$ $$1.1760$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 