# Properties

 Label 221067.q Number of curves $2$ Conductor $221067$ CM no Rank $0$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 221067.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.q1 221067q1 $$[0, 0, 1, -68970, 10505250]$$ $$-28094464000/20657483$$ $$-26678477614662027$$ $$[]$$ $$1209600$$ $$1.8513$$ $$\Gamma_0(N)$$-optimal
221067.q2 221067q2 $$[0, 0, 1, 562650, -162148077]$$ $$15252992000000/17621717267$$ $$-22757883409104720723$$ $$[]$$ $$3628800$$ $$2.4006$$

## Rank

sage: E.rank()

The elliptic curves in class 221067.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 221067.q do not have complex multiplication.

## Modular form 221067.2.a.q

sage: E.q_eigenform(10)

$$q - 2q^{4} - q^{7} - 2q^{13} + 4q^{16} + 6q^{17} + 7q^{19} + O(q^{20})$$ ## 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. 