Properties

Label 13860.c
Number of curves $2$
Conductor $13860$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13860.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.c1 13860a1 \([0, 0, 0, -34368, 2452333]\) \(10392086293512192/1684375\) \(727650000\) \([2]\) \(24960\) \(1.1024\) \(\Gamma_0(N)\)-optimal
13860.c2 13860a2 \([0, 0, 0, -34263, 2468062]\) \(-643570518871152/8271484375\) \(-57172500000000\) \([2]\) \(49920\) \(1.4489\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13860.2.a.c

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