Properties

Label 50820.e
Number of curves $2$
Conductor $50820$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 50820.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50820.e1 50820e2 \([0, -1, 0, -62476, -5979224]\) \(59466754384/121275\) \(55000591430400\) \([2]\) \(230400\) \(1.5230\)  
50820.e2 50820e1 \([0, -1, 0, -2581, -157430]\) \(-67108864/343035\) \(-9723318842160\) \([2]\) \(115200\) \(1.1764\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 50820.e have rank \(0\).

Complex multiplication

The elliptic curves in class 50820.e do not have complex multiplication.

Modular form 50820.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} + 6q^{13} + q^{15} - 2q^{17} + O(q^{20})\)  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.