Properties

Label 24200.n
Number of curves $4$
Conductor $24200$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 24200.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24200.n1 24200h4 \([0, 0, 0, -323675, 70875750]\) \(132304644/5\) \(141724880000000\) \([2]\) \(122880\) \(1.8015\)  
24200.n2 24200h2 \([0, 0, 0, -21175, 998250]\) \(148176/25\) \(177156100000000\) \([2, 2]\) \(61440\) \(1.4549\)  
24200.n3 24200h1 \([0, 0, 0, -6050, -166375]\) \(55296/5\) \(2214451250000\) \([2]\) \(30720\) \(1.1083\) \(\Gamma_0(N)\)-optimal
24200.n4 24200h3 \([0, 0, 0, 39325, 5656750]\) \(237276/625\) \(-17715610000000000\) \([2]\) \(122880\) \(1.8015\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24200.n have rank \(2\).

Complex multiplication

The elliptic curves in class 24200.n do not have complex multiplication.

Modular form 24200.2.a.n

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - 3 q^{9} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.