Properties

Label 102921e
Number of curves $6$
Conductor $102921$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("102921.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 102921e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102921.l5 102921e1 [1, 1, 0, -132499, 19820728] [2] 884736 \(\Gamma_0(N)\)-optimal
102921.l4 102921e2 [1, 1, 0, -2161344, 1222114275] [2, 2] 1769472  
102921.l3 102921e3 [1, 1, 0, -2202749, 1172800920] [2, 2] 3538944  
102921.l1 102921e4 [1, 1, 0, -34581459, 78258791538] [2] 3538944  
102921.l6 102921e5 [1, 1, 0, 2109286, 5209728087] [2] 7077888  
102921.l2 102921e6 [1, 1, 0, -7177264, -6019352867] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 102921e have rank \(0\).

Modular form 102921.2.a.l

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.