Properties

Label 14651d
Number of curves $2$
Conductor $14651$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 14651d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14651.j1 14651d1 \([0, -1, 1, -2140679, -1204809558]\) \(-9221261135586623488/121324931\) \(-14273756807219\) \([]\) \(165888\) \(2.0825\) \(\Gamma_0(N)\)-optimal
14651.j2 14651d2 \([0, -1, 1, -2019649, -1347170777]\) \(-7743965038771437568/2189290237869371\) \(-257567807195093628779\) \([]\) \(497664\) \(2.6318\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14651d have rank \(0\).

Complex multiplication

The elliptic curves in class 14651d do not have complex multiplication.

Modular form 14651.2.a.d

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.