Properties

Label 15210.z
Number of curves $4$
Conductor $15210$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 15210.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.z1 15210z4 \([1, -1, 1, -194213, -32893883]\) \(8527173507/200\) \(19001216309400\) \([2]\) \(103680\) \(1.6600\)  
15210.z2 15210z3 \([1, -1, 1, -11693, -551339]\) \(-1860867/320\) \(-30401946095040\) \([2]\) \(51840\) \(1.3134\)  
15210.z3 15210z2 \([1, -1, 1, -4088, 27317]\) \(57960603/31250\) \(4072620093750\) \([2]\) \(34560\) \(1.1107\)  
15210.z4 15210z1 \([1, -1, 1, 982, 2981]\) \(804357/500\) \(-65161921500\) \([2]\) \(17280\) \(0.76411\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15210.z have rank \(0\).

Complex multiplication

The elliptic curves in class 15210.z do not have complex multiplication.

Modular form 15210.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} - 6 q^{11} - 2 q^{14} + q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.