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Properties

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

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Show commands: SageMath
E = EllipticCurve("jl1")
 
E.isogeny_class()
 

Elliptic curves in class 139650.jl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.jl1 139650v2 \([1, 0, 0, -17924103, -29209657653]\) \(43304971114320697781/296432262\) \(4359369899004750\) \([2]\) \(5308416\) \(2.6009\)  
139650.jl2 139650v1 \([1, 0, 0, -1119553, -457072603]\) \(-10552599539268821/27662978028\) \(-406815212752021500\) \([2]\) \(2654208\) \(2.2543\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 139650.2.a.jl

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.