Properties

Label 4004.c
Number of curves 2
Conductor 4004
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4004.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4004.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4004.c1 4004c1 [0, -1, 0, -21, 38] [2] 840 \(\Gamma_0(N)\)-optimal
4004.c2 4004c2 [0, -1, 0, 44, 168] [2] 1680  

Rank

sage: E.rank()
 

The elliptic curves in class 4004.c have rank \(0\).

Modular form 4004.2.a.c

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

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.