Properties

Label 254898da
Number of curves $4$
Conductor $254898$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 254898da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254898.da4 254898da1 \([1, -1, 0, 124794, 4584917812]\) \(103823/4386816\) \(-9081523591611753590784\) \([2]\) \(21233664\) \(2.8923\) \(\Gamma_0(N)\)-optimal
254898.da3 254898da2 \([1, -1, 0, -40658886, 98020328692]\) \(3590714269297/73410624\) \(151973621353377938995776\) \([2, 2]\) \(42467328\) \(3.2388\)  
254898.da1 254898da3 \([1, -1, 0, -647316126, 6339188682364]\) \(14489843500598257/6246072\) \(12930528707587828843128\) \([2]\) \(84934656\) \(3.5854\)  
254898.da2 254898da4 \([1, -1, 0, -86540526, -163771132820]\) \(34623662831857/14438442312\) \(29890256277572013807210888\) \([2]\) \(84934656\) \(3.5854\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254898da have rank \(1\).

Complex multiplication

The elliptic curves in class 254898da do not have complex multiplication.

Modular form 254898.2.a.da

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2q^{5} - q^{8} - 2q^{10} + 6q^{13} + q^{16} + O(q^{20})\)  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 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.