Properties

Label 377706.ch
Number of curves $6$
Conductor $377706$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("377706.ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 377706.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
377706.ch1 377706ch5 [1, 1, 1, -7257141527, 237952877081573] [2] 346030080  
377706.ch2 377706ch3 [1, 1, 1, -454434287, 3703013813621] [2, 2] 173015040  
377706.ch3 377706ch6 [1, 1, 1, -154787527, 8513782616069] [2] 346030080  
377706.ch4 377706ch2 [1, 1, 1, -47993007, -32181549579] [2, 2] 86507520  
377706.ch5 377706ch1 [1, 1, 1, -37159087, -87092189707] [2] 43253760 \(\Gamma_0(N)\)-optimal
377706.ch6 377706ch4 [1, 1, 1, 185105553, -252879266187] [2] 173015040  

Rank

sage: E.rank()
 

The elliptic curves in class 377706.ch have rank \(1\).

Modular form 377706.2.a.ch

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} - 2q^{13} - q^{14} - 2q^{15} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.