Properties

Label 271440x
Number of curves $6$
Conductor $271440$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 271440x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271440.x4 271440x1 \([0, 0, 0, -1488243, 698650162]\) \(122083727651299441/32242728960\) \(96276272790896640\) \([2]\) \(3932160\) \(2.2432\) \(\Gamma_0(N)\)-optimal
271440.x3 271440x2 \([0, 0, 0, -1672563, 514661938]\) \(173294065906331761/61964605497600\) \(185025320582145638400\) \([2, 2]\) \(7864320\) \(2.5898\)  
271440.x6 271440x3 \([0, 0, 0, 5066637, 3618737458]\) \(4817210305461175439/4682306425314960\) \(-13981292069087665520640\) \([2]\) \(15728640\) \(2.9364\)  
271440.x2 271440x4 \([0, 0, 0, -11360883, -14364659918]\) \(54309086480107021681/1575939143610000\) \(4705729067793162240000\) \([2, 2]\) \(15728640\) \(2.9364\)  
271440.x5 271440x5 \([0, 0, 0, 2753997, -47701183502]\) \(773618103830753999/329643718157812500\) \(-984310868119737600000000\) \([2]\) \(31457280\) \(3.2830\)  
271440.x1 271440x6 \([0, 0, 0, -180488883, -933304735118]\) \(217764763259392950709681/191615146362900\) \(572159761197277593600\) \([2]\) \(31457280\) \(3.2830\)  

Rank

sage: E.rank()
 

The elliptic curves in class 271440x have rank \(0\).

Complex multiplication

The elliptic curves in class 271440x do not have complex multiplication.

Modular form 271440.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{11} + q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.