Properties

Label 96600.i
Number of curves $4$
Conductor $96600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 96600.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.i1 96600b4 \([0, -1, 0, -5520408, 4994188812]\) \(581416486276209698/12425175\) \(397605600000000\) \([2]\) \(1572864\) \(2.3291\)  
96600.i2 96600b2 \([0, -1, 0, -345408, 77938812]\) \(284840777767396/1312250625\) \(20996010000000000\) \([2, 2]\) \(786432\) \(1.9825\)  
96600.i3 96600b3 \([0, -1, 0, -170408, 156688812]\) \(-17101973157698/321306440175\) \(-10281806085600000000\) \([2]\) \(1572864\) \(2.3291\)  
96600.i4 96600b1 \([0, -1, 0, -32908, -186188]\) \(985329269584/566015625\) \(2264062500000000\) \([2]\) \(393216\) \(1.6360\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 96600.i have rank \(0\).

Complex multiplication

The elliptic curves in class 96600.i do not have complex multiplication.

Modular form 96600.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.