Properties

Label 9792bs
Number of curves $4$
Conductor $9792$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 9792bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9792.i4 9792bs1 \([0, 0, 0, -396, 1296]\) \(35937/17\) \(3248750592\) \([2]\) \(4096\) \(0.51924\) \(\Gamma_0(N)\)-optimal
9792.i2 9792bs2 \([0, 0, 0, -3276, -71280]\) \(20346417/289\) \(55228760064\) \([2, 2]\) \(8192\) \(0.86582\)  
9792.i1 9792bs3 \([0, 0, 0, -52236, -4595184]\) \(82483294977/17\) \(3248750592\) \([2]\) \(16384\) \(1.2124\)  
9792.i3 9792bs4 \([0, 0, 0, -396, -192240]\) \(-35937/83521\) \(-15961111658496\) \([2]\) \(16384\) \(1.2124\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9792bs have rank \(1\).

Complex multiplication

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

Modular form 9792.2.a.bs

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 4 q^{7} + 2 q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.