Properties

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

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 139650bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.hm1 139650bj1 \([1, 0, 0, -3199848, -2211406128]\) \(-1231922871794037145/5186378855952\) \(-15254307150597421200\) \([]\) \(4976640\) \(2.5357\) \(\Gamma_0(N)\)-optimal
139650.hm2 139650bj2 \([1, 0, 0, 7483377, -11658267783]\) \(15757536948921630455/29083977048526848\) \(-85542520394553378508800\) \([]\) \(14929920\) \(3.0850\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 139650.2.a.bj

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