# Properties

 Label 1170.n Number of curves $4$ Conductor $1170$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 1170.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.n1 1170n3 $$[1, -1, 1, -778757, -264320611]$$ $$71647584155243142409/10140000$$ $$7392060000$$ $$$$ $$10240$$ $$1.7466$$
1170.n2 1170n4 $$[1, -1, 1, -55877, -2815459]$$ $$26465989780414729/10571870144160$$ $$7706893335092640$$ $$$$ $$10240$$ $$1.7466$$
1170.n3 1170n2 $$[1, -1, 1, -48677, -4120099]$$ $$17496824387403529/6580454400$$ $$4797151257600$$ $$[2, 2]$$ $$5120$$ $$1.4000$$
1170.n4 1170n1 $$[1, -1, 1, -2597, -83491]$$ $$-2656166199049/2658140160$$ $$-1937784176640$$ $$$$ $$2560$$ $$1.0534$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1170.n have rank $$0$$.

## Complex multiplication

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

## Modular form1170.2.a.n

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 