Properties

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

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

Elliptic curves in class 8550.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.q1 8550b2 $$[1, -1, 0, -13542, 604116]$$ $$651038076963/7220000$$ $$3045937500000$$ $$$$ $$30720$$ $$1.2097$$
8550.q2 8550b1 $$[1, -1, 0, -1542, -7884]$$ $$961504803/486400$$ $$205200000000$$ $$$$ $$15360$$ $$0.86315$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form8550.2.a.q

sage: E.q_eigenform(10)

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