Properties

Label 32340.bp
Number of curves $2$
Conductor $32340$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32340.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bp1 32340bp2 \([0, 1, 0, -25300, -1554652]\) \(59466754384/121275\) \(3652577913600\) \([2]\) \(92160\) \(1.2970\)  
32340.bp2 32340bp1 \([0, 1, 0, -1045, -41140]\) \(-67108864/343035\) \(-645723595440\) \([2]\) \(46080\) \(0.95045\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32340.bp have rank \(0\).

Complex multiplication

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

Modular form 32340.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + q^{11} + 6q^{13} + q^{15} - 2q^{17} + O(q^{20})\)  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.