Properties

Label 242550be
Number of curves $4$
Conductor $242550$
CM no
Rank $1$
Graph

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

Elliptic curves in class 242550be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
242550.be4 242550be1 \([1, -1, 0, 2827683, 2435950341]\) \(1865864036231/2993760000\) \(-4011924725077500000000\) \([2]\) \(11796480\) \(2.8305\) \(\Gamma_0(N)\)-optimal
242550.be3 242550be2 \([1, -1, 0, -19222317, 24860800341]\) \(586145095611769/140040608400\) \(187667808827312756250000\) \([2, 2]\) \(23592960\) \(3.1770\)  
242550.be1 242550be3 \([1, -1, 0, -287129817, 1872618827841]\) \(1953542217204454969/170843779260\) \(228947003814225788437500\) \([2]\) \(47185920\) \(3.5236\)  
242550.be2 242550be4 \([1, -1, 0, -104114817, -387971427159]\) \(93137706732176569/5369647977540\) \(7195841846392201911562500\) \([2]\) \(47185920\) \(3.5236\)  

Rank

sage: E.rank()
 

The elliptic curves in class 242550be have rank \(1\).

Complex multiplication

The elliptic curves in class 242550be do not have complex multiplication.

Modular form 242550.2.a.be

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