Properties

Label 259920.c
Number of curves $4$
Conductor $259920$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("259920.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 259920.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259920.c1 259920c4 [0, 0, 0, -158032443, -764658453782] [2] 26542080  
259920.c2 259920c3 [0, 0, 0, -11437563, -7921335638] [2] 26542080  
259920.c3 259920c2 [0, 0, 0, -9878043, -11945209142] [2, 2] 13271040  
259920.c4 259920c1 [0, 0, 0, -520923, -246937718] [2] 6635520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 259920.c have rank \(0\).

Modular form 259920.2.a.c

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.