Properties

Label 3150.bp
Number of curves 8
Conductor 3150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3150.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.bp1 3150bk7 [1, -1, 1, -432180005, 3458268326247] [2] 393216  
3150.bp2 3150bk5 [1, -1, 1, -27011255, 54040488747] [2, 2] 196608  
3150.bp3 3150bk8 [1, -1, 1, -26842505, 54748901247] [2] 393216  
3150.bp4 3150bk3 [1, -1, 1, -3390755, -2401706253] [2] 98304  
3150.bp5 3150bk4 [1, -1, 1, -1698755, 833613747] [2, 2] 98304  
3150.bp6 3150bk2 [1, -1, 1, -240755, -26606253] [2, 2] 49152  
3150.bp7 3150bk1 [1, -1, 1, 47245, -2990253] [2] 24576 \(\Gamma_0(N)\)-optimal
3150.bp8 3150bk6 [1, -1, 1, 285745, 2663322747] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 3150.bp have rank \(0\).

Modular form 3150.2.a.bp

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{7} + q^{8} + 4q^{11} + 2q^{13} + q^{14} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.