# Properties

 Label 3360.l Number of curves $4$ Conductor $3360$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.l1 3360o2 $$[0, -1, 0, -680, -6600]$$ $$68017239368/39375$$ $$20160000$$ $$[2]$$ $$1024$$ $$0.34719$$
3360.l2 3360o3 $$[0, -1, 0, -400, 3172]$$ $$13858588808/229635$$ $$117573120$$ $$[2]$$ $$1024$$ $$0.34719$$
3360.l3 3360o1 $$[0, -1, 0, -50, -48]$$ $$220348864/99225$$ $$6350400$$ $$[2, 2]$$ $$512$$ $$0.00061629$$ $$\Gamma_0(N)$$-optimal
3360.l4 3360o4 $$[0, -1, 0, 175, -543]$$ $$143877824/108045$$ $$-442552320$$ $$[4]$$ $$1024$$ $$0.34719$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.l

sage: E.q_eigenform(10)

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

## 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.