# Properties

 Label 1152.k Number of curves $2$ Conductor $1152$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 1152.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.k1 1152p1 $$[0, 0, 0, -30, 52]$$ $$16000/3$$ $$559872$$ $$$$ $$128$$ $$-0.17914$$ $$\Gamma_0(N)$$-optimal
1152.k2 1152p2 $$[0, 0, 0, 60, 304]$$ $$4000/9$$ $$-53747712$$ $$$$ $$256$$ $$0.16743$$

## Rank

sage: E.rank()

The elliptic curves in class 1152.k have rank $$1$$.

## Complex multiplication

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

## Modular form1152.2.a.k

sage: E.q_eigenform(10)

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

## 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. 