# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 1152.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.p1 1152m2 $$[0, 0, 0, -24, -32]$$ $$3456$$ $$442368$$ $$$$ $$128$$ $$-0.21042$$
1152.p2 1152m1 $$[0, 0, 0, -9, 10]$$ $$23328$$ $$3456$$ $$$$ $$64$$ $$-0.55700$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1152.2.a.p

sage: E.q_eigenform(10)

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