↑

Properties

Label 80850a
Number of curves $2$
Conductor $80850$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 80850a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.s2 80850a1 \([1, 1, 0, 6100, 90000]\) \(668944031/475200\) \(-17827425000000\) \([]\) \(290304\) \(1.2311\) \(\Gamma_0(N)\)-optimal
80850.s1 80850a2 \([1, 1, 0, -67400, -8215500]\) \(-902612375329/249562500\) \(-9362493164062500\) \([]\) \(870912\) \(1.7804\)  

Rank

sage: E.rank()
 

The elliptic curves in class 80850a have rank \(1\).

Complex multiplication

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

Modular form 80850.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.