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Properties

Label 157794.bv
Number of curves $2$
Conductor $157794$
CM no
Rank $0$
Graph

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

Elliptic curves in class 157794.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157794.bv1 157794bc2 \([1, 1, 1, -1061929350, -13320053728587]\) \(-5486773802537974663600129/2635437714\) \(-63613059666877266\) \([]\) \(41489280\) \(3.4632\)  
157794.bv2 157794bc1 \([1, 1, 1, 206340, -407533347]\) \(40251338884511/2997011332224\) \(-72340567825338723456\) \([]\) \(5927040\) \(2.4902\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 157794.bv have rank \(0\).

Complex multiplication

The elliptic curves in class 157794.bv do not have complex multiplication.

Modular form 157794.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 5 q^{11} - q^{12} - q^{13} - q^{14} - q^{15} + q^{16} + q^{18} - q^{19} + O(q^{20})\) 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.