Properties

Label 100011d
Number of curves 2
Conductor 100011
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100011.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100011d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100011.d1 100011d1 [1, 0, 1, -692, 6941] [2] 45312 \(\Gamma_0(N)\)-optimal
100011.d2 100011d2 [1, 0, 1, -647, 7895] [2] 90624  

Rank

sage: E.rank()
 

The elliptic curves in class 100011d have rank \(1\).

Modular form 100011.2.a.d

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} + 2q^{7} - 3q^{8} + q^{9} - 2q^{10} - 6q^{11} - q^{12} + 2q^{13} + 2q^{14} - 2q^{15} - q^{16} - q^{17} + q^{18} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.