Properties

Label 369600.fj
Number of curves $4$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.fj1 369600fj4 \([0, -1, 0, -2957633, -1956796863]\) \(1397097631688978/433125\) \(887040000000000\) \([2]\) \(6291456\) \(2.2307\)  
369600.fj2 369600fj2 \([0, -1, 0, -185633, -30256863]\) \(690862540036/12006225\) \(12294374400000000\) \([2, 2]\) \(3145728\) \(1.8841\)  
369600.fj3 369600fj1 \([0, -1, 0, -23633, 685137]\) \(5702413264/2525985\) \(646652160000000\) \([2]\) \(1572864\) \(1.5376\) \(\Gamma_0(N)\)-optimal
369600.fj4 369600fj3 \([0, -1, 0, -5633, -86596863]\) \(-9653618/1581886845\) \(-3239704258560000000\) \([2]\) \(6291456\) \(2.2307\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.fj have rank \(0\).

Complex multiplication

The elliptic curves in class 369600.fj do not have complex multiplication.

Modular form 369600.2.a.fj

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + q^{11} + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.