Properties

Label 8550.i
Number of curves $2$
Conductor $8550$
CM no
Rank $1$
Graph

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

Elliptic curves in class 8550.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.i1 8550a2 \([1, -1, 0, -7467, 249191]\) \(149721291/722\) \(222048843750\) \([2]\) \(12288\) \(1.0258\)  
8550.i2 8550a1 \([1, -1, 0, -717, -559]\) \(132651/76\) \(23373562500\) \([2]\) \(6144\) \(0.67927\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8550.i have rank \(1\).

Complex multiplication

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

Modular form 8550.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} + 2q^{11} + 4q^{13} + q^{16} - q^{19} + O(q^{20})\)  Toggle raw display

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.