# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("i1")

E.isogeny_class()

## Elliptic curves in class 16245.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.i1 16245e2 $$[0, 0, 1, -946542, 263932605]$$ $$7575076864/1953125$$ $$24181674720486328125$$ $$[3]$$ $$344736$$ $$2.4286$$
16245.i2 16245e1 $$[0, 0, 1, -329232, -72686538]$$ $$318767104/125$$ $$1547627182111125$$ $$[]$$ $$114912$$ $$1.8793$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form16245.2.a.i

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.