Properties

Label 3150b
Number of curves $4$
Conductor $3150$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3150.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.g3 3150b1 [1, -1, 0, -1167, 13741] [2] 2304 \(\Gamma_0(N)\)-optimal
3150.g4 3150b2 [1, -1, 0, 1833, 70741] [2] 4608  
3150.g1 3150b3 [1, -1, 0, -23667, -1393759] [2] 6912  
3150.g2 3150b4 [1, -1, 0, -16917, -2210509] [2] 13824  

Rank

sage: E.rank()
 

The elliptic curves in class 3150b have rank \(1\).

Modular form 3150.2.a.g

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.