Properties

Label 31850.bg
Number of curves $2$
Conductor $31850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 31850.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31850.bg1 31850m1 \([1, 1, 0, -1030250, 402012500]\) \(65787589563409/10400000\) \(19117962500000000\) \([2]\) \(552960\) \(2.1346\) \(\Gamma_0(N)\)-optimal
31850.bg2 31850m2 \([1, 1, 0, -932250, 481686500]\) \(-48743122863889/26406250000\) \(-48541701660156250000\) \([2]\) \(1105920\) \(2.4812\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31850.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 31850.bg do not have complex multiplication.

Modular form 31850.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - q^{8} + q^{9} - 2 q^{11} + 2 q^{12} - q^{13} + q^{16} + 2 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) 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.