Properties

Label 87120fy
Number of curves $4$
Conductor $87120$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120fy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.fp4 87120fy1 \([0, 0, 0, 238128, 164337239]\) \(72268906496/606436875\) \(-12531100788527310000\) \([2]\) \(1105920\) \(2.3459\) \(\Gamma_0(N)\)-optimal
87120.fp3 87120fy2 \([0, 0, 0, -3437247, 2258565914]\) \(13584145739344/1195803675\) \(395351588729596435200\) \([2]\) \(2211840\) \(2.6925\)  
87120.fp2 87120fy3 \([0, 0, 0, -17011632, 27027819731]\) \(-26348629355659264/24169921875\) \(-499434878636718750000\) \([2]\) \(3317760\) \(2.8952\)  
87120.fp1 87120fy4 \([0, 0, 0, -272246007, 1728981679106]\) \(6749703004355978704/5671875\) \(1875211490988000000\) \([2]\) \(6635520\) \(3.2418\)  

Rank

sage: E.rank()
 

The elliptic curves in class 87120fy have rank \(1\).

Complex multiplication

The elliptic curves in class 87120fy do not have complex multiplication.

Modular form 87120.2.a.fy

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2q^{7} - 2q^{13} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.