Properties

Label 19600.cj
Number of curves $4$
Conductor $19600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 19600.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.cj1 19600h4 \([0, 0, 0, -366275, 85321250]\) \(1443468546/7\) \(26353376000000\) \([2]\) \(98304\) \(1.7756\)  
19600.cj2 19600h3 \([0, 0, 0, -72275, -5916750]\) \(11090466/2401\) \(9039207968000000\) \([2]\) \(98304\) \(1.7756\)  
19600.cj3 19600h2 \([0, 0, 0, -23275, 1286250]\) \(740772/49\) \(92236816000000\) \([2, 2]\) \(49152\) \(1.4291\)  
19600.cj4 19600h1 \([0, 0, 0, 1225, 85750]\) \(432/7\) \(-3294172000000\) \([2]\) \(24576\) \(1.0825\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19600.cj have rank \(0\).

Complex multiplication

The elliptic curves in class 19600.cj do not have complex multiplication.

Modular form 19600.2.a.cj

sage: E.q_eigenform(10)
 
\(q - 3q^{9} + 4q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.