Properties

Label 64757e
Number of curves $4$
Conductor $64757$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64757e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64757.h4 64757e1 \([1, -1, 0, 491407, 150999776]\) \(22062729659823/29354283343\) \(-17460612303658242103\) \([2]\) \(1128960\) \(2.3780\) \(\Gamma_0(N)\)-optimal
64757.h3 64757e2 \([1, -1, 0, -3044998, 1479980775]\) \(5249244962308257/1448621666569\) \(861673950581127255649\) \([2, 2]\) \(2257920\) \(2.7246\)  
64757.h2 64757e3 \([1, -1, 0, -17800343, -27720846980]\) \(1048626554636928177/48569076788309\) \(28890019553125973354189\) \([2]\) \(4515840\) \(3.0712\)  
64757.h1 64757e4 \([1, -1, 0, -44872133, 115693155606]\) \(16798320881842096017/2132227789307\) \(1268298814764078028547\) \([4]\) \(4515840\) \(3.0712\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64757e have rank \(0\).

Complex multiplication

The elliptic curves in class 64757e do not have complex multiplication.

Modular form 64757.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 2q^{5} - q^{7} - 3q^{8} - 3q^{9} - 2q^{10} + q^{11} + 6q^{13} - q^{14} - q^{16} + 2q^{17} - 3q^{18} + 8q^{19} + O(q^{20})\)  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.