Properties

Label 15600z
Number of curves $6$
Conductor $15600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15600.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15600z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15600.n6 15600z1 [0, -1, 0, 5992, -73488] [2] 36864 \(\Gamma_0(N)\)-optimal
15600.n5 15600z2 [0, -1, 0, -26008, -585488] [2, 2] 73728  
15600.n2 15600z3 [0, -1, 0, -338008, -75465488] [2] 147456  
15600.n3 15600z4 [0, -1, 0, -226008, 41014512] [2, 2] 147456  
15600.n1 15600z5 [0, -1, 0, -3606008, 2636854512] [2] 294912  
15600.n4 15600z6 [0, -1, 0, -46008, 104374512] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 15600z have rank \(0\).

Modular form 15600.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} - 4q^{11} - q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.