# Properties

 Label 18480.bg Number of curves $6$ Conductor $18480$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 18480.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18480.bg1 18480cd5 [0, -1, 0, -48787200, 131177938752] [4] 491520
18480.bg2 18480cd4 [0, -1, 0, -3049200, 2050417152] [2, 4] 245760
18480.bg3 18480cd6 [0, -1, 0, -3034080, 2071742400] [4] 491520
18480.bg4 18480cd3 [0, -1, 0, -407120, -52590720] [2] 245760
18480.bg5 18480cd2 [0, -1, 0, -191520, 31752000] [2, 2] 122880
18480.bg6 18480cd1 [0, -1, 0, 560, 1480192] [2] 61440 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 18480.bg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 18480.bg do not have complex multiplication.

## Modular form 18480.2.a.bg

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - q^{7} + q^{9} + q^{11} - 2q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.