Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13860.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.e1 13860l2 \([0, 0, 0, -16383, -777418]\) \(2605772594896/108945375\) \(20331821664000\) \([2]\) \(27648\) \(1.3185\)  
13860.e2 13860l1 \([0, 0, 0, 492, -45043]\) \(1129201664/75796875\) \(-884094750000\) \([2]\) \(13824\) \(0.97190\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13860.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + q^{11} + 4q^{13} - 2q^{17} - 6q^{19} + O(q^{20})\)  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.