Properties

Label 39600.cj
Number of curves $4$
Conductor $39600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 39600.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.cj1 39600cy4 \([0, 0, 0, -213075, 37847250]\) \(22930509321/6875\) \(320760000000000\) \([2]\) \(196608\) \(1.7615\)  
39600.cj2 39600cy3 \([0, 0, 0, -105075, -12804750]\) \(2749884201/73205\) \(3415452480000000\) \([2]\) \(196608\) \(1.7615\)  
39600.cj3 39600cy2 \([0, 0, 0, -15075, 425250]\) \(8120601/3025\) \(141134400000000\) \([2, 2]\) \(98304\) \(1.4149\)  
39600.cj4 39600cy1 \([0, 0, 0, 2925, 47250]\) \(59319/55\) \(-2566080000000\) \([2]\) \(49152\) \(1.0684\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 39600.cj have rank \(1\).

Complex multiplication

The elliptic curves in class 39600.cj do not have complex multiplication.

Modular form 39600.2.a.cj

sage: E.q_eigenform(10)
 
\(q - q^{11} - 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.