Properties

Label 316050de
Number of curves $2$
Conductor $316050$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("de1")
 
E.isogeny_class()
 

Elliptic curves in class 316050de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
316050.de1 316050de1 \([1, 0, 1, -234001, -40189852]\) \(770842973809/66873600\) \(122931440100000000\) \([2]\) \(4423680\) \(2.0200\) \(\Gamma_0(N)\)-optimal
316050.de2 316050de2 \([1, 0, 1, 255999, -186209852]\) \(1009328859791/8734528080\) \(-16056382720061250000\) \([2]\) \(8847360\) \(2.3665\)  

Rank

sage: E.rank()
 

The elliptic curves in class 316050de have rank \(2\).

Complex multiplication

The elliptic curves in class 316050de do not have complex multiplication.

Modular form 316050.2.a.de

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