Properties

Label 76664.j
Number of curves $2$
Conductor $76664$
CM no
Rank $0$
Graph

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

Elliptic curves in class 76664.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.j1 76664i2 \([0, -1, 0, -2004672, -1067303380]\) \(169556172914/4353013\) \(22873375565456009216\) \([2]\) \(2363904\) \(2.4969\)  
76664.j2 76664i1 \([0, -1, 0, 21448, -53432932]\) \(415292/469567\) \(-1233695183559580672\) \([2]\) \(1181952\) \(2.1504\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 76664.j have rank \(0\).

Complex multiplication

The elliptic curves in class 76664.j do not have complex multiplication.

Modular form 76664.2.a.j

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + 2q^{5} - q^{7} + q^{9} + 4q^{11} + 6q^{13} + 4q^{15} + 4q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.