↑

Properties

Label 286110d
Number of curves $2$
Conductor $286110$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 286110d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.d2 286110d1 \([1, -1, 0, 40185, -39611075]\) \(2003711812543/190316544000\) \(-681633356709888000\) \([2]\) \(5406720\) \(2.1014\) \(\Gamma_0(N)\)-optimal
286110.d1 286110d2 \([1, -1, 0, -1526535, -701080259]\) \(109842365774994497/4216608000000\) \(15102106230816000000\) \([2]\) \(10813440\) \(2.4480\)  

Rank

sage: E.rank()
 

The elliptic curves in class 286110d have rank \(0\).

Complex multiplication

The elliptic curves in class 286110d do not have complex multiplication.

Modular form 286110.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - 4 q^{7} - q^{8} + q^{10} - q^{11} - 4 q^{13} + 4 q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) 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.