Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("176400.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.ci1 176400dw7 [0, 0, 0, -338829123675, 75913534493914250] [2] 452984832  
176400.ci2 176400dw5 [0, 0, 0, -21176823675, 1186148571214250] [2, 2] 226492416  
176400.ci3 176400dw8 [0, 0, 0, -21044523675, 1201700568514250] [2] 452984832  
176400.ci4 176400dw4 [0, 0, 0, -2658351675, -52740864121750] [2] 113246208  
176400.ci5 176400dw3 [0, 0, 0, -1331823675, 18290166214250] [2, 2] 113246208  
176400.ci6 176400dw2 [0, 0, 0, -188751675, -585381721750] [2, 2] 56623104  
176400.ci7 176400dw1 [0, 0, 0, 37040325, -65382745750] [2] 28311552 \(\Gamma_0(N)\)-optimal
176400.ci8 176400dw6 [0, 0, 0, 224024325, 58466829118250] [2] 226492416  

Rank

sage: E.rank()
 

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

Modular form 176400.2.a.ci

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

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 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.