# Properties

 Label 47432.n Number of curves $4$ Conductor $47432$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 47432.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47432.n1 47432g4 [0, 0, 0, -1772771, 908500670] [2] 491520
47432.n2 47432g3 [0, 0, 0, -349811, -63001554] [2] 491520
47432.n3 47432g2 [0, 0, 0, -112651, 13695990] [2, 2] 245760
47432.n4 47432g1 [0, 0, 0, 5929, 913066] [2] 122880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 47432.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 47432.n do not have complex multiplication.

## Modular form 47432.2.a.n

sage: E.q_eigenform(10)

$$q - 2q^{5} - 3q^{9} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.