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Properties

Label 14586.h
Number of curves $2$
Conductor $14586$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 14586.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.h1 14586g1 \([1, 0, 1, -94, -256]\) \(90458382169/25788048\) \(25788048\) \([2]\) \(6400\) \(0.12875\) \(\Gamma_0(N)\)-optimal
14586.h2 14586g2 \([1, 0, 1, 246, -1616]\) \(1656015369191/2114999172\) \(-2114999172\) \([2]\) \(12800\) \(0.47533\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14586.h have rank \(0\).

Complex multiplication

The elliptic curves in class 14586.h do not have complex multiplication.

Modular form 14586.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 4 q^{5} - q^{6} - q^{8} + q^{9} - 4 q^{10} + q^{11} + q^{12} - q^{13} + 4 q^{15} + q^{16} + q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.