# Properties

 Label 30960.s Number of curves $2$ Conductor $30960$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 30960.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.s1 30960bn2 $$[0, 0, 0, -34203, -2356918]$$ $$1481933914201/53916840$$ $$160994821570560$$ $$$$ $$110592$$ $$1.4958$$
30960.s2 30960bn1 $$[0, 0, 0, -5403, 102602]$$ $$5841725401/1857600$$ $$5546763878400$$ $$$$ $$55296$$ $$1.1492$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30960.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 30960.s do not have complex multiplication.

## Modular form 30960.2.a.s

sage: E.q_eigenform(10)

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