# Properties

 Label 16245.l Number of curves $2$ Conductor $16245$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("l1")

E.isogeny_class()

## Elliptic curves in class 16245.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.l1 16245f2 $$[1, -1, 0, -271359, 43167438]$$ $$9393931/2025$$ $$476359646653804275$$ $$[2]$$ $$194560$$ $$2.1061$$
16245.l2 16245f1 $$[1, -1, 0, 37296, 4091715]$$ $$24389/45$$ $$-10585769925640095$$ $$[2]$$ $$97280$$ $$1.7596$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 16245.l have rank $$1$$.

## Complex multiplication

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

## Modular form16245.2.a.l

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{5} + 2 q^{7} - 3 q^{8} + q^{10} + 4 q^{11} + 2 q^{13} + 2 q^{14} - q^{16} - 6 q^{17} + O(q^{20})$$

## 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.