Properties

Label 127050.gr
Number of curves $8$
Conductor $127050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("127050.gr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 127050.gr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
127050.gr1 127050gb8 [1, 1, 1, -19514338, -20882966719] [2] 19906560  
127050.gr2 127050gb5 [1, 1, 1, -17427088, -28009019719] [2] 6635520  
127050.gr3 127050gb6 [1, 1, 1, -8170588, 8746908281] [2, 2] 9953280  
127050.gr4 127050gb3 [1, 1, 1, -8110088, 8886300281] [2] 4976640  
127050.gr5 127050gb2 [1, 1, 1, -1092088, -435539719] [2, 2] 3317760  
127050.gr6 127050gb4 [1, 1, 1, -245088, -1092811719] [2] 6635520  
127050.gr7 127050gb1 [1, 1, 1, -124088, 5868281] [2] 1658880 \(\Gamma_0(N)\)-optimal
127050.gr8 127050gb7 [1, 1, 1, 2205162, 29456905281] [2] 19906560  

Rank

sage: E.rank()
 

The elliptic curves in class 127050.gr have rank \(0\).

Modular form 127050.2.a.gr

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.