Properties

Label 38640.c
Number of curves $4$
Conductor $38640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38640.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.c1 38640d4 \([0, -1, 0, -97296256, 324018123616]\) \(49737293673675178002921218/6641736806881023047235\) \(13602276980492335200737280\) \([2]\) \(8847360\) \(3.5503\)  
38640.c2 38640d2 \([0, -1, 0, -93934856, 350444105856]\) \(89516703758060574923008036/1985322833430374025\) \(2032970581432703001600\) \([2, 2]\) \(4423680\) \(3.2038\)  
38640.c3 38640d1 \([0, -1, 0, -93934356, 350448022656]\) \(358061097267989271289240144/176126855625\) \(45088475040000\) \([2]\) \(2211840\) \(2.8572\) \(\Gamma_0(N)\)-optimal
38640.c4 38640d3 \([0, -1, 0, -90581456, 376619404896]\) \(-40133926989810174413190818/6689384645060302103835\) \(-13699859753083498708654080\) \([2]\) \(8847360\) \(3.5503\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38640.c have rank \(0\).

Complex multiplication

The elliptic curves in class 38640.c do not have complex multiplication.

Modular form 38640.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - 4 q^{11} - 2 q^{13} + q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.