# Properties

 Label 2070.k Number of curves $2$ Conductor $2070$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 2070.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.k1 2070o2 $$[1, -1, 1, -28548518, 57983424981]$$ $$3529773792266261468365081/50841342773437500000$$ $$37063338881835937500000$$ $$[2]$$ $$276480$$ $$3.1346$$
2070.k2 2070o1 $$[1, -1, 1, -204998, 2452800597]$$ $$-1306902141891515161/3564268498800000000$$ $$-2598351735625200000000$$ $$[2]$$ $$138240$$ $$2.7880$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2070.2.a.k

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - 2q^{7} + q^{8} - q^{10} - 2q^{11} - 2q^{13} - 2q^{14} + q^{16} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.