Properties

Label 100016.g
Number of curves 2
Conductor 100016
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100016.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100016.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100016.g1 100016m1 [0, 0, 0, -5171, -142350] [2] 80640 \(\Gamma_0(N)\)-optimal
100016.g2 100016m2 [0, 0, 0, -2131, -308334] [2] 161280  

Rank

sage: E.rank()
 

The elliptic curves in class 100016.g have rank \(1\).

Modular form 100016.2.a.g

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - q^{7} - 3q^{9} + 2q^{11} - 6q^{13} + 2q^{17} + q^{19} + O(q^{20}) \)

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 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.