Properties

Label 38962e
Number of curves $2$
Conductor $38962$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 38962e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38962.d2 38962e1 \([1, 0, 1, -1576, -173274]\) \(-244140625/7169008\) \(-12700334981488\) \([2]\) \(92160\) \(1.1948\) \(\Gamma_0(N)\)-optimal
38962.d1 38962e2 \([1, 0, 1, -57236, -5249466]\) \(11704814052625/66001628\) \(116925910101308\) \([2]\) \(184320\) \(1.5414\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38962e have rank \(2\).

Complex multiplication

The elliptic curves in class 38962e do not have complex multiplication.

Modular form 38962.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{12} + 2 q^{13} + q^{14} + q^{16} + 4 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.