# Properties

 Label 10320y Number of curves $2$ Conductor $10320$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 10320y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10320.p2 10320y1 $$[0, -1, 0, -600, -3600]$$ $$5841725401/1857600$$ $$7608729600$$ $$$$ $$6912$$ $$0.59988$$ $$\Gamma_0(N)$$-optimal
10320.p1 10320y2 $$[0, -1, 0, -3800, 88560]$$ $$1481933914201/53916840$$ $$220843376640$$ $$$$ $$13824$$ $$0.94645$$

## Rank

sage: E.rank()

The elliptic curves in class 10320y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 10320y do not have complex multiplication.

## Modular form 10320.2.a.y

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{11} - 2q^{13} - q^{15} - 4q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 