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Properties

Label 151725.be
Number of curves $2$
Conductor $151725$
CM no
Rank $1$
Graph

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

Elliptic curves in class 151725.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
151725.be1 151725r2 \([1, 0, 0, -9038023588, -292914453060583]\) \(216486375407331255135001/27004994294227023375\) \(10184920517523610599666802734375\) \([2]\) \(278691840\) \(4.6795\)  
151725.be2 151725r1 \([1, 0, 0, 837648287, -23693762076208]\) \(172343644217341694999/742780064187984375\) \(-280139141424404715976318359375\) \([2]\) \(139345920\) \(4.3330\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 151725.be have rank \(1\).

Complex multiplication

The elliptic curves in class 151725.be do not have complex multiplication.

Modular form 151725.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + q^{7} + 3 q^{8} + q^{9} - q^{12} - 4 q^{13} - q^{14} - q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.