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Properties

Label 335730.bg
Number of curves $2$
Conductor $335730$
CM no
Rank $2$
Graph

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

Elliptic curves in class 335730.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
335730.bg1 335730bg2 \([1, 0, 1, -238629, 44847556]\) \(31942518433489/27900\) \(1312580079900\) \([2]\) \(2304000\) \(1.6256\)  
335730.bg2 335730bg1 \([1, 0, 1, -14809, 710252]\) \(-7633736209/230640\) \(-10850661993840\) \([2]\) \(1152000\) \(1.2791\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 335730.bg have rank \(2\).

Complex multiplication

The elliptic curves in class 335730.bg do not have complex multiplication.

Modular form 335730.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{10} + q^{12} - 4 q^{13} + 2 q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) 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.