# Properties

 Label 3120.y Number of curves $2$ Conductor $3120$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 3120.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.y1 3120x2 $$[0, 1, 0, -13640, 608628]$$ $$68523370149961/243360$$ $$996802560$$ $$$$ $$3840$$ $$0.94498$$
3120.y2 3120x1 $$[0, 1, 0, -840, 9588]$$ $$-16022066761/998400$$ $$-4089446400$$ $$$$ $$1920$$ $$0.59841$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3120.y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3120.y do not have complex multiplication.

## Modular form3120.2.a.y

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 