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Properties

Label 479408y
Number of curves $2$
Conductor $479408$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 479408y have rank \(0\).

Complex multiplication

The elliptic curves in class 479408y do not have complex multiplication.

Modular form 479408.2.a.y

Copy content sage:E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} + q^{9} - 4 q^{11} + 6 q^{13} - 4 q^{15} - 2 q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.

Elliptic curves in class 479408y

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479408.y1 479408y1 \([0, -1, 0, -153184, -16639680]\) \(300763/83\) \(109703491238531072\) \([2]\) \(4936960\) \(1.9772\) \(\Gamma_0(N)\)-optimal
479408.y2 479408y2 \([0, -1, 0, 395536, -109263616]\) \(5177717/6889\) \(-9105389772798078976\) \([2]\) \(9873920\) \(2.3238\)