Properties

Label 1950.b
Number of curves $4$
Conductor $1950$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.b1 1950a4 \([1, 1, 0, -29900, -1901250]\) \(189208196468929/10860320250\) \(169692503906250\) \([2]\) \(6912\) \(1.4845\)  
1950.b2 1950a2 \([1, 1, 0, -5150, 139500]\) \(967068262369/4928040\) \(77000625000\) \([2]\) \(2304\) \(0.93524\)  
1950.b3 1950a1 \([1, 1, 0, -150, 4500]\) \(-24137569/561600\) \(-8775000000\) \([2]\) \(1152\) \(0.58866\) \(\Gamma_0(N)\)-optimal
1950.b4 1950a3 \([1, 1, 0, 1350, -120000]\) \(17394111071/411937500\) \(-6436523437500\) \([2]\) \(3456\) \(1.1380\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1950.b have rank \(1\).

Complex multiplication

The elliptic curves in class 1950.b do not have complex multiplication.

Modular form 1950.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 2q^{7} - q^{8} + q^{9} - q^{12} - q^{13} + 2q^{14} + q^{16} - q^{18} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.