Properties

Label 17136.bk
Number of curves $4$
Conductor $17136$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17136.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17136.bk1 17136bl4 \([0, 0, 0, -731379, 240747442]\) \(14489843500598257/6246072\) \(18650671054848\) \([2]\) \(147456\) \(1.8890\)  
17136.bk2 17136bl3 \([0, 0, 0, -97779, -6220622]\) \(34623662831857/14438442312\) \(43112957728555008\) \([2]\) \(147456\) \(1.8890\)  
17136.bk3 17136bl2 \([0, 0, 0, -45939, 3722290]\) \(3590714269297/73410624\) \(219202948694016\) \([2, 2]\) \(73728\) \(1.5424\)  
17136.bk4 17136bl1 \([0, 0, 0, 141, 174130]\) \(103823/4386816\) \(-13098962386944\) \([2]\) \(36864\) \(1.1959\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17136.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 17136.bk do not have complex multiplication.

Modular form 17136.2.a.bk

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.