Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

Elliptic curves in class 8550.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.bg1 8550u2 $$[1, -1, 1, -9980, 215647]$$ $$260549802603/104256800$$ $$43983337500000$$ $$$$ $$30720$$ $$1.3160$$
8550.bg2 8550u1 $$[1, -1, 1, 2020, 23647]$$ $$2161700757/1848320$$ $$-779760000000$$ $$$$ $$15360$$ $$0.96945$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form8550.2.a.bg

sage: E.q_eigenform(10)

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