Properties

Label 87120.f
Number of curves $4$
Conductor $87120$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.f1 87120ew4 \([0, 0, 0, -7732263, 8275761362]\) \(154639330142416/33275\) \(11001240747129600\) \([2]\) \(2488320\) \(2.4627\)  
87120.f2 87120ew3 \([0, 0, 0, -484968, 128352323]\) \(610462990336/8857805\) \(183033142930368720\) \([2]\) \(1244160\) \(2.1161\)  
87120.f3 87120ew2 \([0, 0, 0, -109263, 7855562]\) \(436334416/171875\) \(56824590636000000\) \([2]\) \(829440\) \(1.9134\)  
87120.f4 87120ew1 \([0, 0, 0, -49368, -4135417]\) \(643956736/15125\) \(312535248498000\) \([2]\) \(414720\) \(1.5668\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.f have rank \(0\).

Complex multiplication

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

Modular form 87120.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4q^{7} + 4q^{13} - 4q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.