Properties

Label 950e
Number of curves $3$
Conductor $950$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 950e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
950.d2 950e1 \([1, 1, 1, -388, 2781]\) \(-413493625/152\) \(-2375000\) \([]\) \(288\) \(0.19128\) \(\Gamma_0(N)\)-optimal
950.d3 950e2 \([1, 1, 1, 237, 11281]\) \(94196375/3511808\) \(-54872000000\) \([]\) \(864\) \(0.74058\)  
950.d1 950e3 \([1, 1, 1, -2138, -306969]\) \(-69173457625/2550136832\) \(-39845888000000\) \([]\) \(2592\) \(1.2899\)  

Rank

sage: E.rank()
 

The elliptic curves in class 950e have rank \(1\).

Complex multiplication

The elliptic curves in class 950e do not have complex multiplication.

Modular form 950.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} - 2q^{9} - 6q^{11} - q^{12} - 5q^{13} + q^{14} + q^{16} - 3q^{17} - 2q^{18} + q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.