Properties

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

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

Elliptic curves in class 369600eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.eg3 369600eg1 \([0, -1, 0, -25988033, -50984064063]\) \(473897054735271721/779625\) \(3193344000000000\) \([2]\) \(14155776\) \(2.6668\) \(\Gamma_0(N)\)-optimal
369600.eg2 369600eg2 \([0, -1, 0, -25996033, -50951096063]\) \(474334834335054841/607815140625\) \(2489610816000000000000\) \([2, 2]\) \(28311552\) \(3.0133\)  
369600.eg1 369600eg3 \([0, -1, 0, -33124033, -20778272063]\) \(981281029968144361/522287841796875\) \(2139291000000000000000000\) \([2]\) \(56623104\) \(3.3599\)  
369600.eg4 369600eg4 \([0, -1, 0, -18996033, -79014096063]\) \(-185077034913624841/551466161890875\) \(-2258805399105024000000000\) \([2]\) \(56623104\) \(3.3599\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 369600.2.a.eg

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 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.