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Properties

Label 13950.bg
Number of curves $2$
Conductor $13950$
CM no
Rank $0$
Graph

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

Elliptic curves in class 13950.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13950.bg1 13950o2 \([1, -1, 0, -452817, 41207341]\) \(901456690969801/457629750000\) \(5212688871093750000\) \([2]\) \(368640\) \(2.2839\)  
13950.bg2 13950o1 \([1, -1, 0, 105183, 4937341]\) \(11298232190519/7472736000\) \(-85119133500000000\) \([2]\) \(184320\) \(1.9374\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13950.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 13950.bg do not have complex multiplication.

Modular form 13950.2.a.bg

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.