Properties

Label 202800.je
Number of curves $2$
Conductor $202800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("je1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 202800.je

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
202800.je1 202800ih2 \([0, 1, 0, -846408, -295432812]\) \(434163602/7605\) \(1174652238240000000\) \([2]\) \(3096576\) \(2.2638\)  
202800.je2 202800ih1 \([0, 1, 0, -1408, -13202812]\) \(-4/975\) \(-75298220400000000\) \([2]\) \(1548288\) \(1.9172\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 202800.je have rank \(0\).

Complex multiplication

The elliptic curves in class 202800.je do not have complex multiplication.

Modular form 202800.2.a.je

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.