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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 143745.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143745.j1 143745g4 \([1, 0, 0, -154041, -23281500]\) \(157551496201/13125\) \(33675159118125\) \([2]\) \(829440\) \(1.6395\)  
143745.j2 143745g2 \([1, 0, 0, -10296, -311049]\) \(47045881/11025\) \(28287133659225\) \([2, 2]\) \(414720\) \(1.2929\)  
143745.j3 143745g1 \([1, 0, 0, -3451, 73640]\) \(1771561/105\) \(269401272945\) \([2]\) \(207360\) \(0.94635\) \(\Gamma_0(N)\)-optimal
143745.j4 143745g3 \([1, 0, 0, 23929, -1933314]\) \(590589719/972405\) \(-2494925188743645\) \([2]\) \(829440\) \(1.6395\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 143745.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + q^{7} + 3 q^{8} + q^{9} + q^{10} - q^{12} + 6 q^{13} - q^{14} - q^{15} - q^{16} - 2 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.