# Properties

 Label 2160.s Number of curves $2$ Conductor $2160$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2160.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2160.s1 2160p1 $$[0, 0, 0, -72, 236]$$ $$-5971968/25$$ $$-172800$$ $$[]$$ $$288$$ $$-0.14004$$ $$\Gamma_0(N)$$-optimal
2160.s2 2160p2 $$[0, 0, 0, 168, 1244]$$ $$8429568/15625$$ $$-972000000$$ $$[]$$ $$864$$ $$0.40927$$

## Rank

sage: E.rank()

The elliptic curves in class 2160.s have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2160.s do not have complex multiplication.

## Modular form2160.2.a.s

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 6 q^{11} - q^{13} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 