Properties

Label 14490.z
Number of curves 8
Conductor 14490
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("14490.z1")
sage: E.isogeny_class()

Elliptic curves in class 14490.z

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
14490.z1 14490bb7 [1, -1, 0, -2285091144, 39448430519400] 6 15925248  
14490.z2 14490bb6 [1, -1, 0, -2245670064, 40961041011648] 12 7962624  
14490.z3 14490bb3 [1, -1, 0, -2245667184, 40961151325440] 6 3981312  
14490.z4 14490bb8 [1, -1, 0, -2206295064, 42466591386648] 6 15925248  
14490.z5 14490bb4 [1, -1, 0, -425852784, -3370791981312] 2 5308416  
14490.z6 14490bb2 [1, -1, 0, -39541104, 3795068160] 4 2654208  
14490.z7 14490bb1 [1, -1, 0, -27744624, 56107738368] 2 1327104 \(\Gamma_0(N)\)-optimal
14490.z8 14490bb5 [1, -1, 0, 158026896, 30229666560] 2 5308416  

Rank

sage: E.rank()

The elliptic curves in class 14490.z have rank \(1\).

Modular form 14490.2.a.z

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

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.