Properties

Label 10560.bz
Number of curves $4$
Conductor $10560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10560.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10560.bz1 10560cn4 \([0, 1, 0, -999985, 384558383]\) \(6749703004355978704/5671875\) \(92928000000\) \([2]\) \(55296\) \(1.8401\)  
10560.bz2 10560cn3 \([0, 1, 0, -62485, 5995883]\) \(-26348629355659264/24169921875\) \(-24750000000000\) \([2]\) \(27648\) \(1.4936\)  
10560.bz3 10560cn2 \([0, 1, 0, -12625, 498575]\) \(13584145739344/1195803675\) \(19592047411200\) \([2]\) \(18432\) \(1.2908\)  
10560.bz4 10560cn1 \([0, 1, 0, 875, 36875]\) \(72268906496/606436875\) \(-620991360000\) \([2]\) \(9216\) \(0.94425\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10560.bz have rank \(1\).

Complex multiplication

The elliptic curves in class 10560.bz do not have complex multiplication.

Modular form 10560.2.a.bz

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2q^{7} + q^{9} + q^{11} - 2q^{13} + q^{15} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.