Properties

Label 15870.u
Number of curves 8
Conductor 15870
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15870.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15870.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15870.u1 15870u8 [1, 0, 1, -2821433, 1823881556] [2] 304128  
15870.u2 15870u7 [1, 0, 1, -239913, 6135988] [2] 304128  
15870.u3 15870u6 [1, 0, 1, -176433, 28455556] [2, 2] 152064  
15870.u4 15870u4 [1, 0, 1, -152628, -22963244] [2] 101376  
15870.u5 15870u5 [1, 0, 1, -36248, 2284868] [2] 101376  
15870.u6 15870u2 [1, 0, 1, -9798, -338972] [2, 2] 50688  
15870.u7 15870u3 [1, 0, 1, -7153, 761348] [2] 76032  
15870.u8 15870u1 [1, 0, 1, 782, -25804] [2] 25344 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15870.u have rank \(0\).

Modular form 15870.2.a.u

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.