Properties

Label 1950.g
Number of curves $2$
Conductor $1950$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.g1 1950l2 \([1, 0, 1, -227451, -38491202]\) \(666276475992821/58199166792\) \(113670247640625000\) \([2]\) \(30720\) \(2.0132\)  
1950.g2 1950l1 \([1, 0, 1, -222451, -40401202]\) \(623295446073461/5458752\) \(10661625000000\) \([2]\) \(15360\) \(1.6667\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1950.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 4q^{7} - q^{8} + q^{9} + 2q^{11} + q^{12} - q^{13} + 4q^{14} + q^{16} - 4q^{17} - q^{18} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.