Properties

Label 96600.ce
Number of curves $2$
Conductor $96600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 96600.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.ce1 96600ct2 \([0, 1, 0, -1832208, 953957088]\) \(170054560416634/1633023\) \(6532092000000000\) \([2]\) \(1259520\) \(2.1963\)  
96600.ce2 96600ct1 \([0, 1, 0, -117208, 14137088]\) \(89036727188/8117781\) \(16235562000000000\) \([2]\) \(629760\) \(1.8497\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 96600.2.a.ce

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.