Properties

Label 9702.bo
Number of curves $2$
Conductor $9702$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9702.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.bo1 9702bt2 \([1, -1, 1, -31869095, 69255238511]\) \(121681065322255375/12702096\) \(373667459353938288\) \([2]\) \(458752\) \(2.8008\)  
9702.bo2 9702bt1 \([1, -1, 1, -1986935, 1088055119]\) \(-29489309167375/303595776\) \(-8931113596410179328\) \([2]\) \(229376\) \(2.4542\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9702.bo have rank \(0\).

Complex multiplication

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

Modular form 9702.2.a.bo

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