Properties

Label 125902.j
Number of curves $2$
Conductor $125902$
CM no
Rank $1$
Graph

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

Elliptic curves in class 125902.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
125902.j1 125902e2 \([1, 1, 0, -67987, 1267725]\) \(234770924809/130960928\) \(19386917400744992\) \([2]\) \(2027520\) \(1.8156\)  
125902.j2 125902e1 \([1, 1, 0, 16653, 167405]\) \(3449795831/2071552\) \(-306664041929728\) \([2]\) \(1013760\) \(1.4690\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 125902.j have rank \(1\).

Complex multiplication

The elliptic curves in class 125902.j do not have complex multiplication.

Modular form 125902.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 4 q^{5} - 2 q^{6} - q^{7} - q^{8} + q^{9} + 4 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{13} + q^{14} - 8 q^{15} + q^{16} + q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.