# Properties

 Label 16245.d Number of curves $2$ Conductor $16245$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("d1")

E.isogeny_class()

## Elliptic curves in class 16245.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.d1 16245l2 $$[1, -1, 1, -246992, -2283816]$$ $$48587168449/28048275$$ $$961956183962945475$$ $$[2]$$ $$230400$$ $$2.1402$$
16245.d2 16245l1 $$[1, -1, 1, 61663, -308424]$$ $$756058031/438615$$ $$-15042936210120135$$ $$[2]$$ $$115200$$ $$1.7936$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 16245.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 16245.d do not have complex multiplication.

## Modular form16245.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 3 q^{8} - q^{10} + 6 q^{11} + 2 q^{14} - q^{16} + 6 q^{17} + O(q^{20})$$

## 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.