Properties

Label 201586d
Number of curves $2$
Conductor $201586$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 201586d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
201586.bv2 201586d1 \([1, 0, 0, 186640, -6005504]\) \(3449795831/2071552\) \(-431757798318128128\) \([2]\) \(4915200\) \(2.0732\) \(\Gamma_0(N)\)-optimal
201586.bv1 201586d2 \([1, 0, 0, -762000, -48694304]\) \(234770924809/130960928\) \(27295188312424162592\) \([2]\) \(9830400\) \(2.4197\)  

Rank

sage: E.rank()
 

The elliptic curves in class 201586d have rank \(2\).

Complex multiplication

The elliptic curves in class 201586d do not have complex multiplication.

Modular form 201586.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.