Properties

Label 143745.t
Number of curves $2$
Conductor $143745$
CM no
Rank $1$
Graph

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

Elliptic curves in class 143745.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143745.t1 143745o2 \([0, 1, 1, -57251, -5290795]\) \(15159227841150976/3026520525\) \(4143306598725\) \([]\) \(435456\) \(1.4196\)  
143745.t2 143745o1 \([0, 1, 1, -1751, 17780]\) \(433937022976/144703125\) \(198098578125\) \([]\) \(145152\) \(0.87030\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 143745.t have rank \(1\).

Complex multiplication

The elliptic curves in class 143745.t do not have complex multiplication.

Modular form 143745.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} - q^{5} + q^{7} + q^{9} - 2 q^{12} + 4 q^{13} - q^{15} + 4 q^{16} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.