Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("3150.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.be1 3150bo1 [1, -1, 1, -1535, -22633] [2] 2560 \(\Gamma_0(N)\)-optimal
3150.be2 3150bo2 [1, -1, 1, -635, -49633] [2] 5120  

Rank

sage: E.rank()
 

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

Modular form 3150.2.a.be

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

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 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.