Properties

Label 12274d
Number of curves 4
Conductor 12274
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("12274.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12274d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12274.f4 12274d1 [1, 1, 0, -1090, -9036] [2] 13824 \(\Gamma_0(N)\)-optimal
12274.f3 12274d2 [1, 1, 0, -15530, -751252] [2] 27648  
12274.f2 12274d3 [1, 1, 0, -37190, 2744672] [2] 41472  
12274.f1 12274d4 [1, 1, 0, -40800, 2175014] [2] 82944  

Rank

sage: E.rank()
 

The elliptic curves in class 12274d have rank \(0\).

Modular form 12274.2.a.f

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.