Properties

Label 127296f
Number of curves $4$
Conductor $127296$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 127296f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127296.cs3 127296f1 \([0, 0, 0, -16104, -683192]\) \(618724784128/87947613\) \(65652541314048\) \([2]\) \(327680\) \(1.3771\) \(\Gamma_0(N)\)-optimal
127296.cs2 127296f2 \([0, 0, 0, -68124, 6162640]\) \(2927363579728/320445801\) \(3827384138612736\) \([2, 2]\) \(655360\) \(1.7237\)  
127296.cs4 127296f3 \([0, 0, 0, 90996, 30667120]\) \(1744147297148/9513325341\) \(-454506196080328704\) \([2]\) \(1310720\) \(2.0702\)  
127296.cs1 127296f4 \([0, 0, 0, -1059564, 419791408]\) \(2753580869496292/39328497\) \(1878948204576768\) \([2]\) \(1310720\) \(2.0702\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127296f have rank \(0\).

Complex multiplication

The elliptic curves in class 127296f do not have complex multiplication.

Modular form 127296.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 4 q^{7} - q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.