Properties

Label 143745k
Number of curves $4$
Conductor $143745$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 143745k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143745.f4 143745k1 \([1, 1, 1, 56785, 3551372]\) \(7892485271/6662775\) \(-17094857774724975\) \([4]\) \(875520\) \(1.8024\) \(\Gamma_0(N)\)-optimal
143745.f3 143745k2 \([1, 1, 1, -278620, 30920420]\) \(932288503609/377330625\) \(968127149486975625\) \([2, 2]\) \(1751040\) \(2.1490\)  
143745.f1 143745k3 \([1, 1, 1, -3872245, 2930257070]\) \(2502660030961609/983934525\) \(2524506795519370725\) \([2]\) \(3502080\) \(2.4956\)  
143745.f2 143745k4 \([1, 1, 1, -2051475, -1110089058]\) \(372144896498089/8194921875\) \(21025927474379296875\) \([2]\) \(3502080\) \(2.4956\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 143745.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} + q^{7} + 3 q^{8} + q^{9} - q^{10} + q^{12} - 2 q^{13} - q^{14} - q^{15} - q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.