Properties

Label 14079.e
Number of curves $4$
Conductor $14079$
CM no
Rank $1$
Graph

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

Elliptic curves in class 14079.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14079.e1 14079d4 \([1, 0, 0, -25097, 1528188]\) \(37159393753/1053\) \(49539312693\) \([2]\) \(28800\) \(1.1539\)  
14079.e2 14079d3 \([1, 0, 0, -7047, -206778]\) \(822656953/85683\) \(4031032221723\) \([2]\) \(28800\) \(1.1539\)  
14079.e3 14079d2 \([1, 0, 0, -1632, 21735]\) \(10218313/1521\) \(71556785001\) \([2, 2]\) \(14400\) \(0.80728\)  
14079.e4 14079d1 \([1, 0, 0, 173, 1880]\) \(12167/39\) \(-1834789359\) \([2]\) \(7200\) \(0.46071\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14079.e have rank \(1\).

Complex multiplication

The elliptic curves in class 14079.e do not have complex multiplication.

Modular form 14079.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} - 4 q^{7} + 3 q^{8} + q^{9} - 2 q^{10} + 4 q^{11} - q^{12} - q^{13} + 4 q^{14} + 2 q^{15} - q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.