Properties

Label 9702.bp
Number of curves $2$
Conductor $9702$
CM no
Rank $1$
Graph

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

Elliptic curves in class 9702.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bp1 9702cc2 \([1, -1, 1, -199435865, 1068707030073]\) \(10228636028672744397625/167006381634183168\) \(14323489535009531322851328\) \([2]\) \(3194880\) \(3.6262\)  
9702.bp2 9702cc1 \([1, -1, 1, -738905, 46848304185]\) \(-520203426765625/11054534935707648\) \(-948104580894629358993408\) \([2]\) \(1597440\) \(3.2796\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9702.bp have rank \(1\).

Complex multiplication

The elliptic curves in class 9702.bp do not have complex multiplication.

Modular form 9702.2.a.bp

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