Properties

Label 8550.m
Number of curves $3$
Conductor $8550$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550.m

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

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} + 6q^{11} - 5q^{13} - q^{14} + q^{16} + 3q^{17} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.