Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13860.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.t1 13860f3 \([0, 0, 0, -59832, -5633091]\) \(75216478666752/326095\) \(102696446160\) \([2]\) \(31104\) \(1.3198\)  
13860.t2 13860f4 \([0, 0, 0, -58887, -5819634]\) \(-4481782160112/310023175\) \(-1562159655302400\) \([2]\) \(62208\) \(1.6663\)  
13860.t3 13860f1 \([0, 0, 0, -1032, -1031]\) \(281370820608/161767375\) \(69883506000\) \([6]\) \(10368\) \(0.77046\) \(\Gamma_0(N)\)-optimal
13860.t4 13860f2 \([0, 0, 0, 4113, -8234]\) \(1113258734352/648484375\) \(-4482324000000\) \([6]\) \(20736\) \(1.1170\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 13860.2.a.t

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.