Properties

Label 1764.j
Number of curves $2$
Conductor $1764$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 1764.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1764.j1 1764j2 \([0, 0, 0, -1281, -17647]\) \(406749952\) \(571536\) \([]\) \(540\) \(0.34427\)  
1764.j2 1764j1 \([0, 0, 0, -21, -7]\) \(1792\) \(571536\) \([]\) \(180\) \(-0.20503\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1764.j have rank \(0\).

Complex multiplication

The elliptic curves in class 1764.j do not have complex multiplication.

Modular form 1764.2.a.j

sage: E.q_eigenform(10)
 
\(q + 3q^{5} + 3q^{11} - 2q^{13} + 3q^{17} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.