# Properties

 Label 8470.t Number of curves $2$ Conductor $8470$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8470.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.t1 8470z1 $$[1, 0, 0, -21601, 3963081]$$ $$-5200020529/28672000$$ $$-6146097836032000$$ $$$$ $$71280$$ $$1.7136$$ $$\Gamma_0(N)$$-optimal
8470.t2 8470z2 $$[1, 0, 0, 191359, -97959575]$$ $$3615170357711/21437500000$$ $$-4595318511437500000$$ $$[]$$ $$213840$$ $$2.2629$$

## Rank

sage: E.rank()

The elliptic curves in class 8470.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8470.t do not have complex multiplication.

## Modular form8470.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - q^{5} - 2q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2q^{12} + 2q^{13} + q^{14} + 2q^{15} + q^{16} + 3q^{17} + q^{18} - 7q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 