Properties

Label 4290.bb
Number of curves 8
Conductor 4290
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4290.bb1")
sage: E.isogeny_class()

Elliptic curves in class 4290.bb

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4290.bb1 4290bb7 [1, 0, 0, -1047000, -231922620] 4 165888  
4290.bb2 4290bb6 [1, 0, 0, -913900, -336246400] 4 82944  
4290.bb3 4290bb3 [1, 0, 0, -913820, -336308208] 2 41472  
4290.bb4 4290bb8 [1, 0, 0, -782080, -436614148] 2 165888  
4290.bb5 4290bb4 [1, 0, 0, -471900, 124722000] 12 55296  
4290.bb6 4290bb2 [1, 0, 0, -31900, 1610000] 12 27648  
4290.bb7 4290bb1 [1, 0, 0, -11420, -450288] 6 13824 \(\Gamma_0(N)\)-optimal
4290.bb8 4290bb5 [1, 0, 0, 80420, 10438352] 6 55296  

Rank

sage: E.rank()

The elliptic curves in class 4290.bb have rank \(1\).

Modular form 4290.2.a.bb

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + q^{13} - 4q^{14} + q^{15} + q^{16} - 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.