Properties

Label 43890s
Number of curves $4$
Conductor $43890$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 43890s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43890.r4 43890s1 \([1, 1, 0, 973, 70941]\) \(101710228704839/2208184902000\) \(-2208184902000\) \([2]\) \(110592\) \(1.0489\) \(\Gamma_0(N)\)-optimal
43890.r3 43890s2 \([1, 1, 0, -20807, 1085889]\) \(996287603460985081/58993920562500\) \(58993920562500\) \([2, 2]\) \(221184\) \(1.3955\)  
43890.r2 43890s3 \([1, 1, 0, -62057, -4614861]\) \(26430597275279725081/6198015706748250\) \(6198015706748250\) \([2]\) \(442368\) \(1.7420\)  
43890.r1 43890s4 \([1, 1, 0, -328037, 72178911]\) \(3903860364706612157401/15001464843750\) \(15001464843750\) \([2]\) \(442368\) \(1.7420\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43890s have rank \(2\).

Complex multiplication

The elliptic curves in class 43890s do not have complex multiplication.

Modular form 43890.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - 6 q^{13} - q^{14} - q^{15} + q^{16} - 6 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.