Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 9702.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.u1 9702e2 \([1, -1, 0, -229371, 42339429]\) \(144106117295241933/247808\) \(2294949888\) \([2]\) \(39424\) \(1.4851\)  
9702.u2 9702e1 \([1, -1, 0, -14331, 664677]\) \(-35148950502093/46137344\) \(-427277942784\) \([2]\) \(19712\) \(1.1385\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9702.2.a.u

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