Properties

Label 16245.c
Number of curves 8
Conductor 16245
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16245.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16245.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16245.c1 16245d7 [1, -1, 1, -7017908, -7154068534] [2] 221184  
16245.c2 16245d5 [1, -1, 1, -438683, -111666094] [2, 2] 110592  
16245.c3 16245d8 [1, -1, 1, -357458, -154357954] [2] 221184  
16245.c4 16245d4 [1, -1, 1, -259988, 51089312] [2] 55296  
16245.c5 16245d3 [1, -1, 1, -32558, -1037644] [2, 2] 55296  
16245.c6 16245d2 [1, -1, 1, -16313, 794792] [2, 2] 27648  
16245.c7 16245d1 [1, -1, 1, -68, 34526] [2] 13824 \(\Gamma_0(N)\)-optimal
16245.c8 16245d6 [1, -1, 1, 113647, -7880038] [2] 110592  

Rank

sage: E.rank()
 

The elliptic curves in class 16245.c have rank \(1\).

Modular form 16245.2.a.c

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.