Properties

Label 248430cn
Number of curves 8
Conductor 248430
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("248430.cn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 248430cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.cn7 248430cn1 [1, 1, 0, 1738838, -664302764] [2] 14155776 \(\Gamma_0(N)\)-optimal
248430.cn6 248430cn2 [1, 1, 0, -8860842, -5957782956] [2, 2] 28311552  
248430.cn5 248430cn3 [1, 1, 0, -62521722, 186008649156] [2, 2] 56623104  
248430.cn4 248430cn4 [1, 1, 0, -124794842, -536494953756] [2] 56623104  
248430.cn2 248430cn5 [1, 1, 0, -994134222, 12064254346656] [2, 2] 113246208  
248430.cn8 248430cn6 [1, 1, 0, 10516698, 594687824424] [2] 113246208  
248430.cn1 248430cn7 [1, 1, 0, -15906144972, 772132424676306] [2] 226492416  
248430.cn3 248430cn8 [1, 1, 0, -987923472, 12222440907006] [2] 226492416  

Rank

sage: E.rank()
 

The elliptic curves in class 248430cn have rank \(1\).

Modular form 248430.2.a.cn

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.