↑

Properties

Label 4002.q
Number of curves $2$
Conductor $4002$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 4002.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.q1 4002n2 \([1, 0, 0, -1233, -16767]\) \(207317019156625/9940968\) \(9940968\) \([2]\) \(2304\) \(0.41590\)  
4002.q2 4002n1 \([1, 0, 0, -73, -295]\) \(-43059012625/11141568\) \(-11141568\) \([2]\) \(1152\) \(0.069325\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4002.q have rank \(0\).

Complex multiplication

The elliptic curves in class 4002.q do not have complex multiplication.

Modular form 4002.2.a.q

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