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Properties

Label 476850.gd
Number of curves $2$
Conductor $476850$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 476850.gd have rank \(0\).

Complex multiplication

The elliptic curves in class 476850.gd do not have complex multiplication.

Modular form 476850.2.a.gd

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 476850.gd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.gd1 476850gd1 \([1, 1, 1, -260973, 51243171]\) \(-3257444411545/2737152\) \(-1651704881587200\) \([]\) \(5280000\) \(1.8478\) \(\Gamma_0(N)\)-optimal
476850.gd2 476850gd2 \([1, 1, 1, 1802487, -431606469]\) \(2747555975/1932612\) \(-455552299806914062500\) \([]\) \(26400000\) \(2.6525\)