Properties

Label 13860.x
Number of curves $4$
Conductor $13860$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13860.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.x1 13860x4 \([0, 0, 0, -446367, -60520826]\) \(52702650535889104/22020583921875\) \(4109569453836000000\) \([6]\) \(248832\) \(2.2687\)  
13860.x2 13860x2 \([0, 0, 0, -384807, -91878194]\) \(33766427105425744/9823275\) \(1833258873600\) \([2]\) \(82944\) \(1.7194\)  
13860.x3 13860x1 \([0, 0, 0, -23952, -1447931]\) \(-130287139815424/2250652635\) \(-26251612334640\) \([2]\) \(41472\) \(1.3728\) \(\Gamma_0(N)\)-optimal
13860.x4 13860x3 \([0, 0, 0, 92688, -6938759]\) \(7549996227362816/6152409907875\) \(-71761709165454000\) \([6]\) \(124416\) \(1.9222\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13860.x have rank \(0\).

Complex multiplication

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

Modular form 13860.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} + q^{11} + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.