Properties

Label 1950.u
Number of curves $2$
Conductor $1950$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.u1 1950u2 \([1, 1, 1, -9098, -311569]\) \(666276475992821/58199166792\) \(7274895849000\) \([2]\) \(6144\) \(1.2085\)  
1950.u2 1950u1 \([1, 1, 1, -8898, -326769]\) \(623295446073461/5458752\) \(682344000\) \([2]\) \(3072\) \(0.86193\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1950.u have rank \(0\).

Complex multiplication

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

Modular form 1950.2.a.u

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.