Properties

Label 177450.cb
Number of curves 8
Conductor 177450
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("177450.cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 177450.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177450.cb1 177450iz8 [1, 1, 0, -1483957400, -22003535520000] [2] 63700992  
177450.cb2 177450iz6 [1, 1, 0, -92749400, -343818168000] [2, 2] 31850496  
177450.cb3 177450iz7 [1, 1, 0, -85989400, -396052688000] [2] 63700992  
177450.cb4 177450iz5 [1, 1, 0, -18410525, -29878254375] [2] 21233664  
177450.cb5 177450iz3 [1, 1, 0, -6221400, -4541880000] [2] 15925248  
177450.cb6 177450iz2 [1, 1, 0, -2440025, 769135125] [2, 2] 10616832  
177450.cb7 177450iz1 [1, 1, 0, -2102025, 1171693125] [2] 5308416 \(\Gamma_0(N)\)-optimal
177450.cb8 177450iz4 [1, 1, 0, 8122475, 5659572625] [2] 21233664  

Rank

sage: E.rank()
 

The elliptic curves in class 177450.cb have rank \(0\).

Modular form 177450.2.a.cb

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.