Properties

Label 9792l
Number of curves $2$
Conductor $9792$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 9792l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9792.j1 9792l1 \([0, 0, 0, -156, -304]\) \(35152/17\) \(203046912\) \([2]\) \(3072\) \(0.28768\) \(\Gamma_0(N)\)-optimal
9792.j2 9792l2 \([0, 0, 0, 564, -2320]\) \(415292/289\) \(-13807190016\) \([2]\) \(6144\) \(0.63425\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9792l have rank \(2\).

Complex multiplication

The elliptic curves in class 9792l do not have complex multiplication.

Modular form 9792.2.a.l

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 2 q^{7} - 6 q^{11} - 2 q^{13} - q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.