# Properties

 Label 1170.e Number of curves $2$ Conductor $1170$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 1170.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.e1 1170e2 $$[1, -1, 0, -414, 3010]$$ $$10779215329/1232010$$ $$898135290$$ $$$$ $$768$$ $$0.45026$$
1170.e2 1170e1 $$[1, -1, 0, 36, 220]$$ $$6967871/35100$$ $$-25587900$$ $$$$ $$384$$ $$0.10369$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1170.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1170.e do not have complex multiplication.

## Modular form1170.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} - 4q^{11} - q^{13} - 2q^{14} + q^{16} - 8q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 