Properties

Label 14415g
Number of curves 8
Conductor 14415
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("14415.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14415g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14415.d7 14415g1 [1, 0, 0, -20, -5553] [2] 7680 \(\Gamma_0(N)\)-optimal
14415.d6 14415g2 [1, 0, 0, -4825, -127600] [2, 2] 15360  
14415.d4 14415g3 [1, 0, 0, -76900, -8214415] [2] 30720  
14415.d5 14415g4 [1, 0, 0, -9630, 167427] [2, 2] 30720  
14415.d2 14415g5 [1, 0, 0, -129755, 17969952] [2, 2] 61440  
14415.d8 14415g6 [1, 0, 0, 33615, 1265850] [2] 61440  
14415.d1 14415g7 [1, 0, 0, -2075780, 1150945707] [2] 122880  
14415.d3 14415g8 [1, 0, 0, -105730, 24836297] [2] 122880  

Rank

sage: E.rank()
 

The elliptic curves in class 14415g have rank \(0\).

Modular form 14415.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + 3q^{8} + q^{9} - q^{10} + 4q^{11} - q^{12} + 2q^{13} + q^{15} - q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.