# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("f1")

E.isogeny_class()

## Elliptic curves in class 16245.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.f1 16245a2 $$[0, 0, 1, -56257518, 162412318188]$$ $$1590409933520896/45$$ $$557145785560005$$ $$[3]$$ $$590976$$ $$2.7901$$
16245.f2 16245a1 $$[0, 0, 1, -699618, 219362823]$$ $$3058794496/91125$$ $$1128220215759010125$$ $$[]$$ $$196992$$ $$2.2408$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form16245.2.a.f

sage: E.q_eigenform(10)

$$q - 2 q^{4} - q^{5} + 2 q^{7} + 3 q^{11} - 4 q^{13} + 4 q^{16} + O(q^{20})$$

## 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.