Properties

Label 25872.j
Number of curves $4$
Conductor $25872$
CM no
Rank $0$
Graph

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

Elliptic curves in class 25872.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25872.j1 25872f4 \([0, -1, 0, -31371384, -47944627632]\) \(14171198121996897746/4077720290568771\) \(982506935224576695048192\) \([2]\) \(4423680\) \(3.3101\)  
25872.j2 25872f2 \([0, -1, 0, -28762624, -59356387376]\) \(21843440425782779332/3100814593569\) \(373563121785650463744\) \([2, 2]\) \(2211840\) \(2.9635\)  
25872.j3 25872f1 \([0, -1, 0, -28761644, -59360635872]\) \(87364831012240243408/1760913\) \(53035431305472\) \([2]\) \(1105920\) \(2.6169\) \(\Gamma_0(N)\)-optimal
25872.j4 25872f3 \([0, -1, 0, -26169544, -70496259056]\) \(-8226100326647904626/4152140742401883\) \(-1000438182303414544521216\) \([2]\) \(4423680\) \(3.3101\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25872.j have rank \(0\).

Complex multiplication

The elliptic curves in class 25872.j do not have complex multiplication.

Modular form 25872.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} + q^{9} - q^{11} + 6q^{13} + 2q^{15} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.