Properties

Label 32340.bg
Number of curves $2$
Conductor $32340$
CM no
Rank $1$
Graph

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

Elliptic curves in class 32340.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bg1 32340bf2 \([0, 1, 0, -204836, -33091836]\) \(31558509702736/2620631475\) \(78928556134982400\) \([2]\) \(331776\) \(1.9844\)  
32340.bg2 32340bf1 \([0, 1, 0, 13459, -2355900]\) \(143225913344/1361505915\) \(-2562876950301360\) \([2]\) \(165888\) \(1.6378\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32340.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 32340.bg do not have complex multiplication.

Modular form 32340.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + q^{11} + 2q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.