Properties

Label 9702.n
Number of curves $4$
Conductor $9702$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 9702.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.n1 9702u4 \([1, -1, 0, -6232662, -5987079050]\) \(312196988566716625/25367712678\) \(2175690315034582038\) \([2]\) \(221184\) \(2.5638\)  
9702.n2 9702u3 \([1, -1, 0, -362952, -106803572]\) \(-61653281712625/21875235228\) \(-1876154071468110588\) \([2]\) \(110592\) \(2.2172\)  
9702.n3 9702u2 \([1, -1, 0, -160092, 12405784]\) \(5290763640625/2291573592\) \(196539377971876632\) \([2]\) \(73728\) \(2.0145\)  
9702.n4 9702u1 \([1, -1, 0, 33948, 1423120]\) \(50447927375/39517632\) \(-3389274007745472\) \([2]\) \(36864\) \(1.6679\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9702.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.