Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9702.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.d1 9702g2 \([1, -1, 0, -11239188, -14499945776]\) \(144106117295241933/247808\) \(269998559373312\) \([2]\) \(275968\) \(2.4580\)  
9702.d2 9702g1 \([1, -1, 0, -702228, -226579760]\) \(-35148950502093/46137344\) \(-50268822690594816\) \([2]\) \(137984\) \(2.1115\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9702.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{5} - q^{8} + 2 q^{10} - q^{11} - 2 q^{13} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\)  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.