Properties

Label 100905g
Number of curves 4
Conductor 100905
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("100905.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100905g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100905.s3 100905g1 [1, 1, 0, -2422, -44489] [2] 120960 \(\Gamma_0(N)\)-optimal
100905.s2 100905g2 [1, 1, 0, -7227, 179424] [2, 2] 241920  
100905.s4 100905g3 [1, 1, 0, 16798, 1145229] [2] 483840  
100905.s1 100905g4 [1, 1, 0, -108132, 13640151] [2] 483840  

Rank

sage: E.rank()
 

The elliptic curves in class 100905g have rank \(0\).

Modular form 100905.2.a.s

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} + q^{7} - 3q^{8} + q^{9} + q^{10} + q^{12} + 6q^{13} + q^{14} - q^{15} - q^{16} - 2q^{17} + q^{18} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.