Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 369600.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.j1 369600j4 \([0, -1, 0, -154929633, -742196692863]\) \(100407751863770656369/166028940000\) \(680054538240000000000\) \([2]\) \(47185920\) \(3.2601\)  
369600.j2 369600j2 \([0, -1, 0, -9777633, -11356372863]\) \(25238585142450289/995844326400\) \(4078978360934400000000\) \([2, 2]\) \(23592960\) \(2.9136\)  
369600.j3 369600j1 \([0, -1, 0, -1585633, 530219137]\) \(107639597521009/32699842560\) \(133938555125760000000\) \([2]\) \(11796480\) \(2.5670\) \(\Gamma_0(N)\)-optimal
369600.j4 369600j3 \([0, -1, 0, 4302367, -41389012863]\) \(2150235484224911/181905111732960\) \(-745083337658204160000000\) \([2]\) \(47185920\) \(3.2601\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.j

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