Properties

Label 155526.bv
Number of curves $2$
Conductor $155526$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 155526.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155526.bv1 155526bh2 \([1, 1, 1, -3655401, 2789363415]\) \(-6329617441/279936\) \(-238896666027844562304\) \([]\) \(7244160\) \(2.6752\)  
155526.bv2 155526bh1 \([1, 1, 1, -26461, -3831703]\) \(-2401/6\) \(-5120384645658534\) \([]\) \(1034880\) \(1.7022\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 155526.bv have rank \(1\).

Complex multiplication

The elliptic curves in class 155526.bv do not have complex multiplication.

Modular form 155526.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 5 q^{11} - q^{12} + q^{15} + q^{16} + 4 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.