Properties

Label 176400gp
Number of curves $6$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("176400.rj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400gp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.rj6 176400gp1 [0, 0, 0, 1760325, 1258038250] [2] 7077888 \(\Gamma_0(N)\)-optimal
176400.rj5 176400gp2 [0, 0, 0, -12351675, 13013334250] [2, 2] 14155776  
176400.rj2 176400gp3 [0, 0, 0, -185223675, 970205598250] [2, 2] 28311552  
176400.rj4 176400gp4 [0, 0, 0, -65271675, -191839985750] [2] 28311552  
176400.rj1 176400gp5 [0, 0, 0, -2963523675, 62095583898250] [2] 56623104  
176400.rj3 176400gp6 [0, 0, 0, -172875675, 1105132194250] [2] 56623104  

Rank

sage: E.rank()
 

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

Modular form 176400.2.a.rj

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.