Properties

 Label 8550i Number of curves $3$ Conductor $8550$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

Elliptic curves in class 8550i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.m2 8550i1 $$[1, -1, 0, -3492, -78584]$$ $$-413493625/152$$ $$-1731375000$$ $$[]$$ $$8640$$ $$0.74058$$ $$\Gamma_0(N)$$-optimal
8550.m3 8550i2 $$[1, -1, 0, 2133, -302459]$$ $$94196375/3511808$$ $$-40001688000000$$ $$[]$$ $$25920$$ $$1.2899$$
8550.m1 8550i3 $$[1, -1, 0, -19242, 8268916]$$ $$-69173457625/2550136832$$ $$-29047652352000000$$ $$[]$$ $$77760$$ $$1.8392$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form8550.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{7} - q^{8} + 6 q^{11} - 5 q^{13} - q^{14} + q^{16} + 3 q^{17} + q^{19} + O(q^{20})$$ 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels. 