# Properties

 Label 2070.r Number of curves $4$ Conductor $2070$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 2070.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.r1 2070q3 $$[1, -1, 1, -95792, -11362309]$$ $$133345896593725369/340006815000$$ $$247864968135000$$ $$$$ $$15360$$ $$1.6384$$
2070.r2 2070q2 $$[1, -1, 1, -8312, -24901]$$ $$87109155423289/49979073600$$ $$36434744654400$$ $$[2, 2]$$ $$7680$$ $$1.2919$$
2070.r3 2070q1 $$[1, -1, 1, -5432, 154811]$$ $$24310870577209/114462720$$ $$83443322880$$ $$$$ $$3840$$ $$0.94530$$ $$\Gamma_0(N)$$-optimal
2070.r4 2070q4 $$[1, -1, 1, 33088, -223621]$$ $$5495662324535111/3207841648920$$ $$-2338516562062680$$ $$$$ $$15360$$ $$1.6384$$

## Rank

sage: E.rank()

The elliptic curves in class 2070.r have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2070.r do not have complex multiplication.

## Modular form2070.2.a.r

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 