Properties

Label 15059.e
Number of curves $3$
Conductor $15059$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 15059.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15059.e1 15059e3 \([0, -1, 1, -10706036, -13479575637]\) \(-52893159101157376/11\) \(-28222990499\) \([]\) \(258300\) \(2.3022\)  
15059.e2 15059e2 \([0, -1, 1, -14146, -1168277]\) \(-122023936/161051\) \(-413212803895859\) \([]\) \(51660\) \(1.4974\)  
15059.e3 15059e1 \([0, -1, 1, -456, 9063]\) \(-4096/11\) \(-28222990499\) \([]\) \(10332\) \(0.69273\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15059.e have rank \(0\).

Complex multiplication

The elliptic curves in class 15059.e do not have complex multiplication.

Modular form 15059.2.a.e

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{9} - 2 q^{10} + q^{11} - 2 q^{12} - 4 q^{13} - 4 q^{14} + q^{15} - 4 q^{16} + 2 q^{17} - 4 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.