Properties

Label 177870.eb
Number of curves 4
Conductor 177870
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("177870.eb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 177870.eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177870.eb1 177870fj3 [1, 0, 1, -195603763, 1052935718888] [2] 35389440  
177870.eb2 177870fj2 [1, 0, 1, -12575533, 15458499956] [2, 2] 17694720  
177870.eb3 177870fj1 [1, 0, 1, -2970553, -1711362292] [2] 8847360 \(\Gamma_0(N)\)-optimal
177870.eb4 177870fj4 [1, 0, 1, 16773017, 76890884816] [2] 35389440  

Rank

sage: E.rank()
 

The elliptic curves in class 177870.eb have rank \(1\).

Modular form 177870.2.a.eb

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.