Properties

Label 14586.i
Number of curves $4$
Conductor $14586$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14586.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.i1 14586k3 \([1, 1, 1, -2509653144, -48392477978535]\) \(1748094148784980747354970849498497/887694600425282263291392\) \(887694600425282263291392\) \([2]\) \(9455616\) \(3.9280\)  
14586.i2 14586k4 \([1, 1, 1, -343304344, 1346305732697]\) \(4474676144192042711273397261697/1806328356954994499451382272\) \(1806328356954994499451382272\) \([2]\) \(9455616\) \(3.9280\)  
14586.i3 14586k2 \([1, 1, 1, -157701784, -747588108199]\) \(433744050935826360922067531137/9612122270219882316693504\) \(9612122270219882316693504\) \([2, 2]\) \(4727808\) \(3.5814\)  
14586.i4 14586k1 \([1, 1, 1, 895336, -35804233639]\) \(79374649975090937760383/553856914190911653543936\) \(-553856914190911653543936\) \([4]\) \(2363904\) \(3.2349\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14586.2.a.i

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