# Properties

 Label 16245.j Number of curves $4$ Conductor $16245$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 16245.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16245.j1 16245c3 $$[1, -1, 0, -19518435, -33185583684]$$ $$23977812996389881/146611125$$ $$5028240714679045125$$ $$[2]$$ $$829440$$ $$2.7757$$
16245.j2 16245c4 $$[1, -1, 0, -4020705, 2513992950]$$ $$209595169258201/41748046875$$ $$1431809687397216796875$$ $$[2]$$ $$829440$$ $$2.7757$$
16245.j3 16245c2 $$[1, -1, 0, -1242810, -497800809]$$ $$6189976379881/456890625$$ $$15669725218875140625$$ $$[2, 2]$$ $$414720$$ $$2.4291$$
16245.j4 16245c1 $$[1, -1, 0, 73035, -34360200]$$ $$1256216039/15582375$$ $$-534420102201636375$$ $$[2]$$ $$207360$$ $$2.0825$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form16245.2.a.j

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.