Properties

Label 4620j
Number of curves $4$
Conductor $4620$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4620j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.j3 4620j1 \([0, 1, 0, -2661, 52740]\) \(-130287139815424/2250652635\) \(-36010442160\) \([6]\) \(5184\) \(0.82354\) \(\Gamma_0(N)\)-optimal
4620.j2 4620j2 \([0, 1, 0, -42756, 3388644]\) \(33766427105425744/9823275\) \(2514758400\) \([6]\) \(10368\) \(1.1701\)  
4620.j4 4620j3 \([0, 1, 0, 10299, 260424]\) \(7549996227362816/6152409907875\) \(-98438558526000\) \([2]\) \(15552\) \(1.3728\)  
4620.j1 4620j4 \([0, 1, 0, -49596, 2224980]\) \(52702650535889104/22020583921875\) \(5637269484000000\) \([2]\) \(31104\) \(1.7194\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4620j have rank \(0\).

Complex multiplication

The elliptic curves in class 4620j do not have complex multiplication.

Modular form 4620.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} - q^{11} + 2q^{13} - q^{15} - 6q^{17} + 8q^{19} + O(q^{20})\)  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.