Properties

Label 24255be
Number of curves $4$
Conductor $24255$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 24255be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24255.i4 24255be1 \([1, -1, 1, -1553, -170544]\) \(-4826809/144375\) \(-12382483719375\) \([2]\) \(36864\) \(1.1927\) \(\Gamma_0(N)\)-optimal
24255.i3 24255be2 \([1, -1, 1, -56678, -5153844]\) \(234770924809/1334025\) \(114414149567025\) \([2, 2]\) \(73728\) \(1.5393\)  
24255.i2 24255be3 \([1, -1, 1, -89753, 1580226]\) \(932288503609/527295615\) \(45224099518859415\) \([2]\) \(147456\) \(1.8859\)  
24255.i1 24255be4 \([1, -1, 1, -905603, -331480614]\) \(957681397954009/31185\) \(2674616483385\) \([2]\) \(147456\) \(1.8859\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24255be have rank \(1\).

Complex multiplication

The elliptic curves in class 24255be do not have complex multiplication.

Modular form 24255.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} - q^{11} + 2 q^{13} - q^{16} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.