Properties

Label 193200.hi
Number of curves $4$
Conductor $193200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("hi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193200.hi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.hi1 193200fs3 \([0, 1, 0, -4637008, 3841759988]\) \(344577854816148242/2716875\) \(86940000000000\) \([2]\) \(2949120\) \(2.2656\)  
193200.hi2 193200fs2 \([0, 1, 0, -290008, 59869988]\) \(168591300897604/472410225\) \(7558563600000000\) \([2, 2]\) \(1474560\) \(1.9191\)  
193200.hi3 193200fs4 \([0, 1, 0, -175008, 107939988]\) \(-18524646126002/146738831715\) \(-4695642614880000000\) \([4]\) \(2949120\) \(2.2656\)  
193200.hi4 193200fs1 \([0, 1, 0, -25508, 92988]\) \(458891455696/264449745\) \(1057798980000000\) \([2]\) \(737280\) \(1.5725\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193200.hi have rank \(1\).

Complex multiplication

The elliptic curves in class 193200.hi do not have complex multiplication.

Modular form 193200.2.a.hi

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.