Properties

Label 14994bi
Number of curves $6$
Conductor $14994$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14994.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14994bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14994.g5 14994bi1 [1, -1, 0, -30977613, 66286809189] [2] 1474560 \(\Gamma_0(N)\)-optimal
14994.g4 14994bi2 [1, -1, 0, -40009293, 24490000485] [2, 2] 2949120  
14994.g2 14994bi3 [1, -1, 0, -378838413, -2818625145435] [2, 2] 5898240  
14994.g6 14994bi4 [1, -1, 0, 154312947, 192501009189] [2] 5898240  
14994.g1 14994bi5 [1, -1, 0, -6049904373, -181120341567411] [2] 11796480  
14994.g3 14994bi6 [1, -1, 0, -129038373, -6480344011779] [2] 11796480  

Rank

sage: E.rank()
 

The elliptic curves in class 14994bi have rank \(0\).

Modular form 14994.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{5} - q^{8} + 2q^{10} - 4q^{11} + 2q^{13} + q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.