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Properties

Label 499280.g
Number of curves $2$
Conductor $499280$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("g1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 499280.g have rank \(1\).

Complex multiplication

The elliptic curves in class 499280.g do not have complex multiplication.

Modular form 499280.2.a.g

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} + 2 q^{7} + q^{9} - 4 q^{11} + 2 q^{13} - 2 q^{15} - 4 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 499280.g

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
499280.g1 499280g2 \([0, 1, 0, -501360, -26426012]\) \(55990084/31205\) \(7767597106721592320\) \([2]\) \(7987200\) \(2.3150\) \(\Gamma_0(N)\)-optimal*
499280.g2 499280g1 \([0, 1, 0, 122740, -3209492]\) \(3286064/1975\) \(-122905017511417600\) \([2]\) \(3993600\) \(1.9685\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 499280.g1.