Properties

Label 28900b
Number of curves $2$
Conductor $28900$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 28900b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28900.f1 28900b1 \([0, 0, 0, -202300, 35005125]\) \(151732224/85\) \(512923341250000\) \([2]\) \(165888\) \(1.7698\) \(\Gamma_0(N)\)-optimal
28900.f2 28900b2 \([0, 0, 0, -166175, 47901750]\) \(-5256144/7225\) \(-697575744100000000\) \([2]\) \(331776\) \(2.1164\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28900b have rank \(0\).

Complex multiplication

The elliptic curves in class 28900b do not have complex multiplication.

Modular form 28900.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.