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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(7\)\(1\)
\(11\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 6 T + 19 T^{2}\) 1.19.ag
\(23\) \( 1 - 2 T + 23 T^{2}\) 1.23.ac
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 9702.2.a.cc

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

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 9702.cc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.cc1 9702bk1 \([1, -1, 1, -1259, -6149]\) \(69426531/34496\) \(109577337408\) \([2]\) \(9216\) \(0.81129\) \(\Gamma_0(N)\)-optimal
9702.cc2 9702bk2 \([1, -1, 1, 4621, -50837]\) \(3436115229/2324168\) \(-7382773107864\) \([2]\) \(18432\) \(1.1579\)