Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9702.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.c1 9702d2 \([1, -1, 0, -2969556, -1968891184]\) \(-61279455929796531/681472\) \(-32205605515776\) \([]\) \(155520\) \(2.1610\)  
9702.c2 9702d1 \([1, -1, 0, -34701, -2994867]\) \(-71285434106859/18863581528\) \(-1222869399715656\) \([3]\) \(51840\) \(1.6117\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9702.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.