# Properties

 Label 2070.q Number of curves $2$ Conductor $2070$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 2070.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.q1 2070s2 $$[1, -1, 1, -15737, 669849]$$ $$591202341974089/79350000000$$ $$57846150000000$$ $$$$ $$7168$$ $$1.3682$$
2070.q2 2070s1 $$[1, -1, 1, 1543, 54681]$$ $$557644990391/2119680000$$ $$-1545246720000$$ $$$$ $$3584$$ $$1.0216$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2070.q have rank $$1$$.

## Complex multiplication

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

## Modular form2070.2.a.q

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - 2q^{7} + q^{8} + q^{10} - 6q^{11} - 2q^{13} - 2q^{14} + q^{16} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 