Properties

Label 452400eg
Number of curves $4$
Conductor $452400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eg1")
 
E.isogeny_class()
 

Elliptic curves in class 452400eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
452400.eg4 452400eg1 \([0, 1, 0, 287592, 66295188]\) \(41102915774831/53367275520\) \(-3415505633280000000\) \([2]\) \(5529600\) \(2.2421\) \(\Gamma_0(N)\)-optimal*
452400.eg3 452400eg2 \([0, 1, 0, -1760408, 643831188]\) \(9427227449071249/2652468249600\) \(169757967974400000000\) \([2, 2]\) \(11059200\) \(2.5887\) \(\Gamma_0(N)\)-optimal*
452400.eg1 452400eg3 \([0, 1, 0, -25888408, 50685303188]\) \(29981943972267024529/4007065140000\) \(256452168960000000000\) \([2]\) \(22118400\) \(2.9353\) \(\Gamma_0(N)\)-optimal*
452400.eg2 452400eg4 \([0, 1, 0, -10400408, -12402568812]\) \(1943993954077461649/87266819409120\) \(5585076442183680000000\) \([2]\) \(22118400\) \(2.9353\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 452400eg1.

Rank

sage: E.rank()
 

The elliptic curves in class 452400eg have rank \(0\).

Complex multiplication

The elliptic curves in class 452400eg do not have complex multiplication.

Modular form 452400.2.a.eg

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