# Properties

 Label 59584bn Number of curves $3$ Conductor $59584$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bn1")

sage: E.isogeny_class()

## Elliptic curves in class 59584bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59584.u3 59584bn1 $$[0, 1, 0, 131, 69]$$ $$32768/19$$ $$-143061184$$ $$[]$$ $$18144$$ $$0.25436$$ $$\Gamma_0(N)$$-optimal
59584.u2 59584bn2 $$[0, 1, 0, -1829, 31429]$$ $$-89915392/6859$$ $$-51645087424$$ $$[]$$ $$54432$$ $$0.80366$$
59584.u1 59584bn3 $$[0, 1, 0, -150789, 22487149]$$ $$-50357871050752/19$$ $$-143061184$$ $$[]$$ $$163296$$ $$1.3530$$

## Rank

sage: E.rank()

The elliptic curves in class 59584bn have rank $$1$$.

## Complex multiplication

The elliptic curves in class 59584bn do not have complex multiplication.

## Modular form 59584.2.a.bn

sage: E.q_eigenform(10)

$$q - 2q^{3} + 3q^{5} + q^{9} - 3q^{11} - 4q^{13} - 6q^{15} + 3q^{17} + q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.