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Properties

Label 102550u
Number of curves $2$
Conductor $102550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 102550u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102550.u2 102550u1 \([1, -1, 1, -6480, -122353]\) \(1925599082121/689423140\) \(10772236562500\) \([2]\) \(165888\) \(1.2015\) \(\Gamma_0(N)\)-optimal
102550.u1 102550u2 \([1, -1, 1, -92230, -10755353]\) \(5552849431422441/1472310350\) \(23004849218750\) \([2]\) \(331776\) \(1.5481\)  

Rank

sage: E.rank()
 

The elliptic curves in class 102550u have rank \(1\).

Complex multiplication

The elliptic curves in class 102550u do not have complex multiplication.

Modular form 102550.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 3 q^{9} + 2 q^{13} + q^{14} + q^{16} - 4 q^{17} - 3 q^{18} - 6 q^{19} + O(q^{20})\) Copy content 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 Cremona 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 Cremona labels.