# Properties

 Label 121680dq Number of curves $2$ Conductor $121680$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dq1")

sage: E.isogeny_class()

## Elliptic curves in class 121680dq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121680.bt2 121680dq1 $$[0, 0, 0, 96837, -32194838]$$ $$6967871/35100$$ $$-505888383021465600$$ $$[2]$$ $$1548288$$ $$2.0793$$ $$\Gamma_0(N)$$-optimal
121680.bt1 121680dq2 $$[0, 0, 0, -1119963, -408672758]$$ $$10779215329/1232010$$ $$17756682244053442560$$ $$[2]$$ $$3096576$$ $$2.4259$$

## Rank

sage: E.rank()

The elliptic curves in class 121680dq have rank $$1$$.

## Complex multiplication

The elliptic curves in class 121680dq do not have complex multiplication.

## Modular form 121680.2.a.dq

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} - 4q^{11} - 8q^{17} - 6q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.