Properties

 Label 8550k Number of curves $2$ Conductor $8550$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

Elliptic curves in class 8550k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.n2 8550k1 $$[1, -1, 0, -17667, 3174741]$$ $$-53540005609/350208000$$ $$-3989088000000000$$ $$$$ $$64512$$ $$1.6770$$ $$\Gamma_0(N)$$-optimal
8550.n1 8550k2 $$[1, -1, 0, -449667, 115926741]$$ $$882774443450089/2166000000$$ $$24672093750000000$$ $$$$ $$129024$$ $$2.0235$$

Rank

sage: E.rank()

The elliptic curves in class 8550k have rank $$1$$.

Complex multiplication

The elliptic curves in class 8550k do not have complex multiplication.

Modular form8550.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2 q^{7} - q^{8} - 4 q^{11} + 6 q^{13} - 2 q^{14} + q^{16} + 4 q^{17} + q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels. 