# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 1170.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.m1 1170m3 $$[1, -1, 1, -4352, 111561]$$ $$12501706118329/2570490$$ $$1873887210$$ $$$$ $$1024$$ $$0.77634$$
1170.m2 1170m2 $$[1, -1, 1, -302, 1401]$$ $$4165509529/1368900$$ $$997928100$$ $$[2, 2]$$ $$512$$ $$0.42977$$
1170.m3 1170m1 $$[1, -1, 1, -122, -471]$$ $$273359449/9360$$ $$6823440$$ $$$$ $$256$$ $$0.083192$$ $$\Gamma_0(N)$$-optimal
1170.m4 1170m4 $$[1, -1, 1, 868, 8889]$$ $$99317171591/106616250$$ $$-77723246250$$ $$$$ $$1024$$ $$0.77634$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1170.2.a.m

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 