Properties

Label 14400ep
Number of curves $4$
Conductor $14400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ep1")
 
E.isogeny_class()
 

Elliptic curves in class 14400ep

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.dx4 14400ep1 \([0, 0, 0, -1740, -38000]\) \(-24389/12\) \(-286654464000\) \([2]\) \(12288\) \(0.90376\) \(\Gamma_0(N)\)-optimal
14400.dx2 14400ep2 \([0, 0, 0, -30540, -2054000]\) \(131872229/18\) \(429981696000\) \([2]\) \(24576\) \(1.2503\)  
14400.dx3 14400ep3 \([0, 0, 0, -16140, 3792400]\) \(-19465109/248832\) \(-5944066965504000\) \([2]\) \(61440\) \(1.7085\)  
14400.dx1 14400ep4 \([0, 0, 0, -476940, 126365200]\) \(502270291349/1889568\) \(45137758519296000\) \([2]\) \(122880\) \(2.0550\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14400ep have rank \(0\).

Complex multiplication

The elliptic curves in class 14400ep do not have complex multiplication.

Modular form 14400.2.a.ep

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - 2 q^{11} + 6 q^{13} + 2 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.