Properties

Label 79560.bk
Number of curves $4$
Conductor $79560$
CM no
Rank $1$
Graph

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

Elliptic curves in class 79560.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79560.bk1 79560bs4 \([0, 0, 0, -562467, 162364174]\) \(26362547147244676/244298925\) \(182368170316800\) \([2]\) \(589824\) \(1.9001\)  
79560.bk2 79560bs2 \([0, 0, 0, -35967, 2413474]\) \(27572037674704/2472575625\) \(461441953440000\) \([2, 2]\) \(294912\) \(1.5535\)  
79560.bk3 79560bs1 \([0, 0, 0, -7842, -224651]\) \(4572531595264/776953125\) \(9062381250000\) \([2]\) \(147456\) \(1.2069\) \(\Gamma_0(N)\)-optimal
79560.bk4 79560bs3 \([0, 0, 0, 40533, 11302774]\) \(9865576607324/79640206425\) \(-59451095535436800\) \([2]\) \(589824\) \(1.9001\)  

Rank

sage: E.rank()
 

The elliptic curves in class 79560.bk have rank \(1\).

Complex multiplication

The elliptic curves in class 79560.bk do not have complex multiplication.

Modular form 79560.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4q^{11} + q^{13} - q^{17} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.