# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 3360p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.i3 3360p1 $$[0, -1, 0, -70, -200]$$ $$601211584/11025$$ $$705600$$ $$[2, 2]$$ $$768$$ $$-0.082988$$ $$\Gamma_0(N)$$-optimal
3360.i1 3360p2 $$[0, -1, 0, -1120, -14060]$$ $$303735479048/105$$ $$53760$$ $$$$ $$1536$$ $$0.26359$$
3360.i2 3360p3 $$[0, -1, 0, -145, 385]$$ $$82881856/36015$$ $$147517440$$ $$$$ $$1536$$ $$0.26359$$
3360.i4 3360p4 $$[0, -1, 0, 0, -648]$$ $$-8/354375$$ $$-181440000$$ $$$$ $$1536$$ $$0.26359$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3360.2.a.p

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} - 4q^{11} + 6q^{13} - q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 