Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 9702.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.z1 9702l2 \([1, -1, 0, -145508253, 675620692613]\) \(-61279455929796531/681472\) \(-3788957283325530624\) \([]\) \(1088640\) \(3.1339\)  
9702.z2 9702l1 \([1, -1, 0, -1700358, 1030640092]\) \(-71285434106859/18863581528\) \(-143869362007147212744\) \([]\) \(362880\) \(2.5846\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9702.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} - q^{8} - 3 q^{10} + q^{11} - 2 q^{13} + q^{16} - 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.