# Properties

 Label 3360.u Number of curves $4$ Conductor $3360$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.u1 3360m3 $$[0, 1, 0, -680, 6600]$$ $$68017239368/39375$$ $$20160000$$ $$$$ $$1024$$ $$0.34719$$
3360.u2 3360m2 $$[0, 1, 0, -400, -3172]$$ $$13858588808/229635$$ $$117573120$$ $$$$ $$1024$$ $$0.34719$$
3360.u3 3360m1 $$[0, 1, 0, -50, 48]$$ $$220348864/99225$$ $$6350400$$ $$[2, 2]$$ $$512$$ $$0.00061629$$ $$\Gamma_0(N)$$-optimal
3360.u4 3360m4 $$[0, 1, 0, 175, 543]$$ $$143877824/108045$$ $$-442552320$$ $$$$ $$1024$$ $$0.34719$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.u

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. 