# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 1170.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.g1 1170g4 $$[1, -1, 0, -10764, 410670]$$ $$189208196468929/10860320250$$ $$7917173462250$$ $$$$ $$2304$$ $$1.2291$$
1170.g2 1170g2 $$[1, -1, 0, -1854, -30132]$$ $$967068262369/4928040$$ $$3592541160$$ $$$$ $$768$$ $$0.67982$$
1170.g3 1170g1 $$[1, -1, 0, -54, -972]$$ $$-24137569/561600$$ $$-409406400$$ $$$$ $$384$$ $$0.33325$$ $$\Gamma_0(N)$$-optimal
1170.g4 1170g3 $$[1, -1, 0, 486, 25920]$$ $$17394111071/411937500$$ $$-300302437500$$ $$$$ $$1152$$ $$0.88256$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1170.2.a.g

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 