# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 1152.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.f1 1152c2 $$[0, 0, 0, -216, 864]$$ $$3456$$ $$322486272$$ $$$$ $$384$$ $$0.33888$$
1152.f2 1152c1 $$[0, 0, 0, -81, -270]$$ $$23328$$ $$2519424$$ $$$$ $$192$$ $$-0.0076923$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1152.2.a.f

sage: E.q_eigenform(10)

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