Properties

Label 162240.fu
Number of curves $4$
Conductor $162240$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fu1")
 
E.isogeny_class()
 

Elliptic curves in class 162240.fu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.fu1 162240br4 \([0, 1, 0, -12936161, 16992756639]\) \(189208196468929/10860320250\) \(13741769759282233344000\) \([2]\) \(9289728\) \(3.0020\)  
162240.fu2 162240br2 \([0, 1, 0, -2228321, -1275402465]\) \(967068262369/4928040\) \(6235542735909027840\) \([2]\) \(3096576\) \(2.4527\)  
162240.fu3 162240br1 \([0, 1, 0, -65121, -41080545]\) \(-24137569/561600\) \(-710603160787353600\) \([2]\) \(1548288\) \(2.1061\) \(\Gamma_0(N)\)-optimal
162240.fu4 162240br3 \([0, 1, 0, 583839, 1085124639]\) \(17394111071/411937500\) \(-521232353181696000000\) \([2]\) \(4644864\) \(2.6554\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162240.fu have rank \(1\).

Complex multiplication

The elliptic curves in class 162240.fu do not have complex multiplication.

Modular form 162240.2.a.fu

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 2 q^{7} + q^{9} - q^{15} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.