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Properties

Label 139650hj
Number of curves $2$
Conductor $139650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("hj1")
 
E.isogeny_class()
 

Elliptic curves in class 139650hj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.a1 139650hj1 \([1, 1, 0, -19058575, -32032722875]\) \(-16658916431011465/106983072\) \(-4916582592862500000\) \([]\) \(8294400\) \(2.7710\) \(\Gamma_0(N)\)-optimal
139650.a2 139650hj2 \([1, 1, 0, -10697950, -60215103500]\) \(-2946301535286265/32373588000768\) \(-1487781349493107200000000\) \([]\) \(24883200\) \(3.3203\)  

Rank

sage: E.rank()
 

The elliptic curves in class 139650hj have rank \(1\).

Complex multiplication

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

Modular form 139650.2.a.hj

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