Properties

Label 102550s
Number of curves 2
Conductor 102550
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("102550.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 102550s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.bb1 102550s1 [1, 1, 1, -1621913, 794409031] [] 2643840 \(\Gamma_0(N)\)-optimal
102550.bb2 102550s2 [1, 1, 1, -120288, 2192385281] [] 7931520  

Rank

sage: E.rank()
 

The elliptic curves in class 102550s have rank \(0\).

Modular form 102550.2.a.bb

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - q^{7} + q^{8} + q^{9} - 6q^{11} + 2q^{12} + q^{13} - q^{14} + q^{16} + 3q^{17} + q^{18} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.