↑

Properties

Label 40362k
Number of curves $2$
Conductor $40362$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 40362k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40362.j1 40362k1 \([1, 1, 0, -66, -252]\) \(-33874537/3024\) \(-2906064\) \([]\) \(10080\) \(-0.016333\) \(\Gamma_0(N)\)-optimal
40362.j2 40362k2 \([1, 1, 0, 399, 213]\) \(7281438503/4214784\) \(-4050407424\) \([]\) \(30240\) \(0.53297\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40362k have rank \(1\).

Complex multiplication

The elliptic curves in class 40362k do not have complex multiplication.

Modular form 40362.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - 3 q^{10} - 3 q^{11} - q^{12} + 4 q^{13} - q^{14} - 3 q^{15} + q^{16} + 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.