# Properties

 Label 1152.s Number of curves $2$ Conductor $1152$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1152.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.s1 1152j1 $$[0, 0, 0, -318, -2180]$$ $$19056256/27$$ $$5038848$$ $$$$ $$384$$ $$0.18920$$ $$\Gamma_0(N)$$-optimal
1152.s2 1152j2 $$[0, 0, 0, -228, -3440]$$ $$-219488/729$$ $$-4353564672$$ $$$$ $$768$$ $$0.53578$$

## Rank

sage: E.rank()

The elliptic curves in class 1152.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1152.s do not have complex multiplication.

## Modular form1152.2.a.s

sage: E.q_eigenform(10)

$$q + 4q^{5} - 2q^{7} + 4q^{11} + 2q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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. 