Properties

Label 179520.fj
Number of curves $4$
Conductor $179520$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fj1")
 
E.isogeny_class()
 

Elliptic curves in class 179520.fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
179520.fj1 179520gc3 \([0, 1, 0, -36348641, 84336968319]\) \(20260414982443110947641/720358602480\) \(188837685488517120\) \([2]\) \(7077888\) \(2.8108\)  
179520.fj2 179520gc2 \([0, 1, 0, -2275041, 1313234559]\) \(4967657717692586041/29490113030400\) \(7730656190241177600\) \([2, 2]\) \(3538944\) \(2.4642\)  
179520.fj3 179520gc4 \([0, 1, 0, -969441, 2811279999]\) \(-384369029857072441/12804787777021680\) \(-3356698287019571281920\) \([2]\) \(7077888\) \(2.8108\)  
179520.fj4 179520gc1 \([0, 1, 0, -227041, -6906241]\) \(4937402992298041/2780405760000\) \(728866687549440000\) \([2]\) \(1769472\) \(2.1176\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 179520.fj have rank \(1\).

Complex multiplication

The elliptic curves in class 179520.fj do not have complex multiplication.

Modular form 179520.2.a.fj

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + q^{11} - 2 q^{13} - q^{15} - q^{17} - 4 q^{19} + O(q^{20})\) 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.