Properties

Label 184093.j
Number of curves $3$
Conductor $184093$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 184093.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
184093.j1 184093j3 \([0, 1, 1, -1661557, 2031201785]\) \(-178643795968/524596891\) \(-1489729715863913531371\) \([]\) \(7962624\) \(2.7497\)  
184093.j2 184093j1 \([0, 1, 1, -103847, -12938565]\) \(-43614208/91\) \(-258418237830571\) \([]\) \(884736\) \(1.6511\) \(\Gamma_0(N)\)-optimal
184093.j3 184093j2 \([0, 1, 1, 179373, -63960648]\) \(224755712/753571\) \(-2139961427474958451\) \([]\) \(2654208\) \(2.2004\)  

Rank

sage: E.rank()
 

The elliptic curves in class 184093.j have rank \(0\).

Complex multiplication

The elliptic curves in class 184093.j do not have complex multiplication.

Modular form 184093.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{4} - 3 q^{5} + q^{9} + 4 q^{12} - q^{13} + 6 q^{15} + 4 q^{16} + 7 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.