# Properties

 Label 283920.dk Number of curves $8$ Conductor $283920$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("283920.dk1")

sage: E.isogeny_class()

## Elliptic curves in class 283920.dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.dk1 283920dk8 [0, -1, 0, -17443560, -17636072208] [2] 31850496
283920.dk2 283920dk5 [0, -1, 0, -15577800, -23659848720] [2] 10616832
283920.dk3 283920dk6 [0, -1, 0, -7303560, 7397559792] [2, 2] 15925248
283920.dk4 283920dk3 [0, -1, 0, -7249480, 7515324400] [2] 7962624
283920.dk5 283920dk2 [0, -1, 0, -976200, -367376400] [2, 2] 5308416
283920.dk6 283920dk4 [0, -1, 0, -219080, -923405328] [2] 10616832
283920.dk7 283920dk1 [0, -1, 0, -110920, 5040112] [2] 2654208 $$\Gamma_0(N)$$-optimal
283920.dk8 283920dk7 [0, -1, 0, 1971160, 24893391600] [2] 31850496

## Rank

sage: E.rank()

The elliptic curves in class 283920.dk have rank $$2$$.

## Modular form 283920.2.a.dk

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.