Properties

Label 274890.ew
Number of curves 6
Conductor 274890
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("274890.ew1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 274890.ew

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
274890.ew1 274890ew5 [1, 0, 0, -14314861, 20842617935] [2] 18874368  
274890.ew2 274890ew3 [1, 0, 0, -974611, 263948285] [2, 2] 9437184  
274890.ew3 274890ew2 [1, 0, 0, -362111, -80644215] [2, 2] 4718592  
274890.ew4 274890ew1 [1, 0, 0, -358191, -82542279] [2] 2359296 \(\Gamma_0(N)\)-optimal
274890.ew5 274890ew4 [1, 0, 0, 187669, -303744939] [2] 9437184  
274890.ew6 274890ew6 [1, 0, 0, 2565639, 1741648635] [2] 18874368  

Rank

sage: E.rank()
 

The elliptic curves in class 274890.ew have rank \(0\).

Modular form 274890.2.a.ew

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.