Properties

 Label 8550f Number of curves $2$ Conductor $8550$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

Elliptic curves in class 8550f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.g2 8550f1 $$[1, -1, 0, -22167, -1388259]$$ $$-105756712489/12476160$$ $$-142111260000000$$ $$$$ $$36864$$ $$1.4514$$ $$\Gamma_0(N)$$-optimal
8550.g1 8550f2 $$[1, -1, 0, -364167, -84494259]$$ $$468898230633769/5540400$$ $$63108618750000$$ $$$$ $$73728$$ $$1.7980$$

Rank

sage: E.rank()

The elliptic curves in class 8550f have rank $$0$$.

Complex multiplication

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

Modular form8550.2.a.f

sage: E.q_eigenform(10)

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