Properties

Label 176400fn
Number of curves 8
Conductor 176400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("176400.lp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400fn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.lp7 176400fn1 [0, 0, 0, -87762675, -316334236750] [2] 21233664 \(\Gamma_0(N)\)-optimal
176400.lp6 176400fn2 [0, 0, 0, -101874675, -207770620750] [2, 2] 42467328  
176400.lp5 176400fn3 [0, 0, 0, -259752675, 1224603553250] [2] 63700992  
176400.lp4 176400fn4 [0, 0, 0, -768666675, 8058449803250] [2] 84934656  
176400.lp8 176400fn5 [0, 0, 0, 339125325, -1525919620750] [2] 84934656  
176400.lp2 176400fn6 [0, 0, 0, -3872424675, 92744423329250] [2, 2] 127401984  
176400.lp1 176400fn7 [0, 0, 0, -61957416675, 5935920363553250] [2] 254803968  
176400.lp3 176400fn8 [0, 0, 0, -3590184675, 106836948769250] [2] 254803968  

Rank

sage: E.rank()
 

The elliptic curves in class 176400fn have rank \(0\).

Modular form 176400.2.a.lp

sage: E.q_eigenform(10)
 
\( q + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.