Properties

Label 10580m
Number of curves 4
Conductor 10580
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("10580.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10580m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10580.c3 10580m1 [0, 1, 0, -705, -5192] [2] 5940 \(\Gamma_0(N)\)-optimal
10580.c4 10580m2 [0, 1, 0, 1940, -32700] [2] 11880  
10580.c1 10580m3 [0, 1, 0, -21865, 1236900] [2] 17820  
10580.c2 10580m4 [0, 1, 0, -19220, 1550068] [2] 35640  

Rank

sage: E.rank()
 

The elliptic curves in class 10580m have rank \(0\).

Modular form 10580.2.a.c

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.