Properties

Label 650.j
Number of curves $3$
Conductor $650$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 650.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
650.j1 650h3 \([1, 1, 1, -11488, -478719]\) \(-10730978619193/6656\) \(-104000000\) \([]\) \(648\) \(0.85911\)  
650.j2 650h2 \([1, 1, 1, -113, -969]\) \(-10218313/17576\) \(-274625000\) \([]\) \(216\) \(0.30980\)  
650.j3 650h1 \([1, 1, 1, 12, 31]\) \(12167/26\) \(-406250\) \([]\) \(72\) \(-0.23951\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 650.j have rank \(0\).

Complex multiplication

The elliptic curves in class 650.j do not have complex multiplication.

Modular form 650.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} - 2 q^{9} + 6 q^{11} - q^{12} - q^{13} + q^{14} + q^{16} + 3 q^{17} - 2 q^{18} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.