Properties

Label 9744.d
Number of curves $4$
Conductor $9744$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 9744.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9744.d1 9744h4 \([0, -1, 0, -92688, 6982848]\) \(21500025903924625/7344878367708\) \(30084621794131968\) \([2]\) \(69120\) \(1.8639\)  
9744.d2 9744h2 \([0, -1, 0, -37968, -2834496]\) \(1477843225692625/274663872\) \(1125023219712\) \([2]\) \(23040\) \(1.3146\)  
9744.d3 9744h1 \([0, -1, 0, -2128, -53312]\) \(-260305116625/157151232\) \(-643691446272\) \([2]\) \(11520\) \(0.96804\) \(\Gamma_0(N)\)-optimal
9744.d4 9744h3 \([0, -1, 0, 17072, 748480]\) \(134335727363375/137728390128\) \(-564135485964288\) \([2]\) \(34560\) \(1.5173\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9744.d have rank \(0\).

Complex multiplication

The elliptic curves in class 9744.d do not have complex multiplication.

Modular form 9744.2.a.d

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.