Properties

Label 10008.f
Number of curves 2
Conductor 10008
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("10008.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10008.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10008.f1 10008f1 [0, 0, 0, -11235, -458354] [2] 10752 \(\Gamma_0(N)\)-optimal
10008.f2 10008f2 [0, 0, 0, -10875, -489098] [2] 21504  

Rank

sage: E.rank()
 

The elliptic curves in class 10008.f have rank \(1\).

Modular form 10008.2.a.f

sage: E.q_eigenform(10)
 
\( q + 4q^{7} - 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20}) \)

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.