Properties

Label 2070.s
Number of curves $2$
Conductor $2070$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2070.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.s1 2070r2 \([1, -1, 1, -6782, 96981]\) \(47316161414809/22001657400\) \(16039208244600\) \([2]\) \(5376\) \(1.2284\)  
2070.s2 2070r1 \([1, -1, 1, 1498, 10869]\) \(510273943271/370215360\) \(-269886997440\) \([2]\) \(2688\) \(0.88179\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2070.s have rank \(0\).

Complex multiplication

The elliptic curves in class 2070.s do not have complex multiplication.

Modular form 2070.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 4q^{7} + q^{8} + q^{10} + 2q^{11} + 4q^{14} + q^{16} - 2q^{17} + O(q^{20})\)  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.