# Properties

 Label 283920.gf Number of curves $6$ Conductor $283920$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("283920.gf1")

sage: E.isogeny_class()

## Elliptic curves in class 283920.gf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.gf1 283920gf5 [0, 1, 0, -45427256, 117833036244] [2] 14155776
283920.gf2 283920gf3 [0, 1, 0, -2839256, 1840359444] [2, 2] 7077888
283920.gf3 283920gf6 [0, 1, 0, -2649976, 2096493140] [2] 14155776
283920.gf4 283920gf4 [0, 1, 0, -1000536, -364417260] [2] 7077888
283920.gf5 283920gf2 [0, 1, 0, -189336, 24634260] [2, 2] 3538944
283920.gf6 283920gf1 [0, 1, 0, 26984, 2396564] [2] 1769472 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 283920.gf have rank $$0$$.

## Modular form 283920.2.a.gf

sage: E.q_eigenform(10)

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

## 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.