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Properties

Label 462550.cj
Number of curves $2$
Conductor $462550$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462550.cj have rank \(0\).

Complex multiplication

The elliptic curves in class 462550.cj do not have complex multiplication.

Modular form 462550.2.a.cj

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{11} + 2 q^{12} + 5 q^{13} - 4 q^{14} + q^{16} + q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 462550.cj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462550.cj1 462550cj2 \([1, 1, 1, -484013, -150286469]\) \(-53969305/10648\) \(-2474093250784375000\) \([]\) \(13471920\) \(2.2524\)  
462550.cj2 462550cj1 \([1, 1, 1, 41612, 1093531]\) \(34295/22\) \(-5111762914843750\) \([]\) \(4490640\) \(1.7031\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 462550.cj1.