Properties

Label 174240.cj
Number of curves $4$
Conductor $174240$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 174240.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
174240.cj1 174240bq2 \([0, 0, 0, -523083, 145614062]\) \(23937672968/45\) \(29755422005760\) \([2]\) \(1474560\) \(1.8406\)  
174240.cj2 174240bq4 \([0, 0, 0, -87483, -6998398]\) \(111980168/32805\) \(21691702642199040\) \([2]\) \(1474560\) \(1.8406\)  
174240.cj3 174240bq1 \([0, 0, 0, -33033, 2225432]\) \(48228544/2025\) \(167374248782400\) \([2, 2]\) \(737280\) \(1.4940\) \(\Gamma_0(N)\)-optimal
174240.cj4 174240bq3 \([0, 0, 0, 15972, 8262848]\) \(85184/5625\) \(-29755422005760000\) \([2]\) \(1474560\) \(1.8406\)  

Rank

sage: E.rank()
 

The elliptic curves in class 174240.cj have rank \(0\).

Complex multiplication

The elliptic curves in class 174240.cj do not have complex multiplication.

Modular form 174240.2.a.cj

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.