# Properties

 Label 283920bp Number of curves 8 Conductor 283920 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("283920.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 283920bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.bp7 283920bp1 [0, -1, 0, -69560456, -222081315600] [2] 37158912 $$\Gamma_0(N)$$-optimal
283920.bp6 283920bp2 [0, -1, 0, -111959176, 80679464176] [2, 2] 74317824
283920.bp5 283920bp3 [0, -1, 0, -429733256, 3279608202480] [2] 111476736
283920.bp4 283920bp4 [0, -1, 0, -1342279176, 18897685672176] [2] 148635648
283920.bp8 283920bp5 [0, -1, 0, 439981304, 639684782320] [2] 148635648
283920.bp2 283920bp6 [0, -1, 0, -6792191176, 215459944884976] [2, 2] 222953472
283920.bp1 283920bp7 [0, -1, 0, -108674990376, 13789346035420656] [2] 445906944
283920.bp3 283920bp8 [0, -1, 0, -6708718696, 221013602702320] [2] 445906944

## Rank

sage: E.rank()

The elliptic curves in class 283920bp have rank $$1$$.

## Modular form 283920.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.