Properties

Label 13860.q
Number of curves $2$
Conductor $13860$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 13860.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.q1 13860t2 \([0, 0, 0, -13042767, 18127933126]\) \(1314817350433665559504/190690249278375\) \(35587377081327456000\) \([2]\) \(645120\) \(2.7665\)  
13860.q2 13860t1 \([0, 0, 0, -740892, 336961501]\) \(-3856034557002072064/1973796785296875\) \(-23022365703702750000\) \([2]\) \(322560\) \(2.4199\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 13860.q have rank \(1\).

Complex multiplication

The elliptic curves in class 13860.q do not have complex multiplication.

Modular form 13860.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + q^{11} + 2q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.