↑

Properties

Label 80850.q
Number of curves $2$
Conductor $80850$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 80850.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.q1 80850n1 \([1, 1, 0, -6118900, 5823029500]\) \(13782741913468081/701662500\) \(1289842054101562500\) \([2]\) \(3317760\) \(2.5451\) \(\Gamma_0(N)\)-optimal
80850.q2 80850n2 \([1, 1, 0, -5788150, 6480891250]\) \(-11666347147400401/3126621093750\) \(-5747560079040527343750\) \([2]\) \(6635520\) \(2.8917\)  

Rank

sage: E.rank()
 

The elliptic curves in class 80850.q have rank \(2\).

Complex multiplication

The elliptic curves in class 80850.q do not have complex multiplication.

Modular form 80850.2.a.q

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