Properties

Label 274890bs
Number of curves $4$
Conductor $274890$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 274890bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.bs4 274890bs1 \([1, 0, 1, -173829, 4561456]\) \(4937402992298041/2780405760000\) \(327111957258240000\) \([2]\) \(3538944\) \(2.0508\) \(\Gamma_0(N)\)-optimal
274890.bs2 274890bs2 \([1, 0, 1, -1741829, -880417744]\) \(4967657717692586041/29490113030400\) \(3469482307913529600\) \([2, 2]\) \(7077888\) \(2.3974\)  
274890.bs3 274890bs3 \([1, 0, 1, -742229, -1883616304]\) \(-384369029857072441/12804787777021680\) \(-1506470477178823630320\) \([2]\) \(14155776\) \(2.7440\)  
274890.bs1 274890bs4 \([1, 0, 1, -27829429, -56509615984]\) \(20260414982443110947641/720358602480\) \(84749469223169520\) \([2]\) \(14155776\) \(2.7440\)  

Rank

sage: E.rank()
 

The elliptic curves in class 274890bs have rank \(0\).

Complex multiplication

The elliptic curves in class 274890bs do not have complex multiplication.

Modular form 274890.2.a.bs

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