Properties

Label 244758.y
Number of curves $2$
Conductor $244758$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 244758.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
244758.y1 244758y1 \([1, 0, 0, -178652951, 542168715753]\) \(13403946614821979039929/5057590268826067968\) \(237938789933949203320439808\) \([2]\) \(227635200\) \(3.7607\) \(\Gamma_0(N)\)-optimal
244758.y2 244758y2 \([1, 0, 0, 558884489, 3869200107593]\) \(410363075617640914325831/374944243169850027552\) \(-17639582245803827184058113312\) \([2]\) \(455270400\) \(4.1073\)  

Rank

sage: E.rank()
 

The elliptic curves in class 244758.y have rank \(0\).

Complex multiplication

The elliptic curves in class 244758.y do not have complex multiplication.

Modular form 244758.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 4q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + 4q^{10} + q^{12} - 4q^{14} + 4q^{15} + q^{16} - 6q^{17} + q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.