Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.cv1 87120bj4 \([0, 0, 0, -8218683, 466677882]\) \(46424454082884/26794860125\) \(35435216471319384192000\) \([2]\) \(8847360\) \(3.0164\)  
87120.cv2 87120bj2 \([0, 0, 0, -5496183, -4941840618]\) \(55537159171536/228765625\) \(75633530136516000000\) \([2, 2]\) \(4423680\) \(2.6698\)  
87120.cv3 87120bj1 \([0, 0, 0, -5490738, -4952154537]\) \(885956203616256/15125\) \(312535248498000\) \([2]\) \(2211840\) \(2.3232\) \(\Gamma_0(N)\)-optimal
87120.cv4 87120bj3 \([0, 0, 0, -2860803, -9690268302]\) \(-1957960715364/29541015625\) \(-39066906062250000000000\) \([2]\) \(8847360\) \(3.0164\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 87120.2.a.cv

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4q^{7} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.