# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 1152.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.t1 1152i1 $$[0, 0, 0, -318, 2180]$$ $$19056256/27$$ $$5038848$$ $$$$ $$384$$ $$0.18920$$ $$\Gamma_0(N)$$-optimal
1152.t2 1152i2 $$[0, 0, 0, -228, 3440]$$ $$-219488/729$$ $$-4353564672$$ $$$$ $$768$$ $$0.53578$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1152.2.a.t

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. 