Properties

Label 9680.g
Number of curves $2$
Conductor $9680$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 9680.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9680.g1 9680r1 \([0, -1, 0, -1976, 93040]\) \(-117649/440\) \(-3192778096640\) \([]\) \(11520\) \(1.0850\) \(\Gamma_0(N)\)-optimal
9680.g2 9680r2 \([0, -1, 0, 17384, -2199184]\) \(80062991/332750\) \(-2414538435584000\) \([]\) \(34560\) \(1.6343\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9680.g have rank \(1\).

Complex multiplication

The elliptic curves in class 9680.g do not have complex multiplication.

Modular form 9680.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} - 2 q^{9} - 2 q^{13} + q^{15} + 3 q^{17} - q^{19} + O(q^{20})\) 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.