# Properties

 Label 58800fj Number of curves 4 Conductor 58800 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.bx1")

sage: E.isogeny_class()

## Elliptic curves in class 58800fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.bx3 58800fj1 [0, -1, 0, -49408, 4021312] [2] 294912 $$\Gamma_0(N)$$-optimal
58800.bx2 58800fj2 [0, -1, 0, -147408, -16754688] [2, 2] 589824
58800.bx4 58800fj3 [0, -1, 0, 342592, -104954688] [2] 1179648
58800.bx1 58800fj4 [0, -1, 0, -2205408, -1259786688] [2] 1179648

## Rank

sage: E.rank()

The elliptic curves in class 58800fj have rank $$1$$.

## Modular form 58800.2.a.bx

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.