Properties

Label 3150.k
Number of curves 2
Conductor 3150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3150.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.k1 3150g2 [1, -1, 0, -36492, 2690666] [2] 11520  
3150.k2 3150g1 [1, -1, 0, -2742, 24416] [2] 5760 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 3150.2.a.k

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.