Properties

Label 115542t
Number of curves $2$
Conductor $115542$
CM no
Rank $0$
Graph

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

Elliptic curves in class 115542t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115542.u2 115542t1 \([1, -1, 0, -941544, 334473376]\) \(1076291879750641/60150618144\) \(5158885193963099424\) \([]\) \(2217600\) \(2.3456\) \(\Gamma_0(N)\)-optimal
115542.u1 115542t2 \([1, -1, 0, -100126854, -385607236694]\) \(1294373635812597347281/2083292441154\) \(178675911586399343634\) \([]\) \(11088000\) \(3.1503\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115542t have rank \(0\).

Complex multiplication

The elliptic curves in class 115542t do not have complex multiplication.

Modular form 115542.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 3 q^{11} - 4 q^{13} + q^{16} - 7 q^{17} + O(q^{20})\) Copy content 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.