↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 139650.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.bi1 139650jd2 \([1, 1, 0, -36775, 2656375]\) \(2992209121/54150\) \(99542083593750\) \([2]\) \(829440\) \(1.4812\)  
139650.bi2 139650jd1 \([1, 1, 0, -25, 120625]\) \(-1/3420\) \(-6286868437500\) \([2]\) \(414720\) \(1.1347\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 139650.2.a.bi

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