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Properties

Label 139650.ja
Number of curves $2$
Conductor $139650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ja1")
 
E.isogeny_class()
 

Elliptic curves in class 139650.ja

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.ja1 139650cj2 \([1, 0, 0, -19843188, 34020853992]\) \(-470056203380406889/1296351000\) \(-2383037481234375000\) \([]\) \(10450944\) \(2.7592\)  
139650.ja2 139650cj1 \([1, 0, 0, -163563, 78131367]\) \(-263251475929/1282741110\) \(-2358018888287343750\) \([]\) \(3483648\) \(2.2099\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 139650.ja have rank \(0\).

Complex multiplication

The elliptic curves in class 139650.ja do not have complex multiplication.

Modular form 139650.2.a.ja

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.