Properties

Label 7098b
Number of curves $6$
Conductor $7098$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7098.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7098b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7098.f5 7098b1 [1, 1, 0, -679, 14773] [2] 7680 \(\Gamma_0(N)\)-optimal
7098.f4 7098b2 [1, 1, 0, -14199, 644805] [2, 2] 15360  
7098.f3 7098b3 [1, 1, 0, -17579, 310185] [2, 2] 30720  
7098.f1 7098b4 [1, 1, 0, -227139, 41571873] [2] 30720  
7098.f2 7098b5 [1, 1, 0, -154469, -23207517] [2] 61440  
7098.f6 7098b6 [1, 1, 0, 65231, 2479807] [2] 61440  

Rank

sage: E.rank()
 

The elliptic curves in class 7098b have rank \(0\).

Modular form 7098.2.a.f

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

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.