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Properties

Label 450800.gb
Number of curves $2$
Conductor $450800$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gb1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 450800.gb have rank \(0\).

Complex multiplication

The elliptic curves in class 450800.gb do not have complex multiplication.

Modular form 450800.2.a.gb

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{9} + 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 450800.gb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450800.gb1 450800gb1 \([0, -1, 0, -49408, 591312]\) \(7086244/4025\) \(7576595600000000\) \([2]\) \(2359296\) \(1.7369\) \(\Gamma_0(N)\)-optimal
450800.gb2 450800gb2 \([0, -1, 0, 195592, 4511312]\) \(219804478/129605\) \(-487932756640000000\) \([2]\) \(4718592\) \(2.0835\)