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Properties

Label 478632j
Number of curves $2$
Conductor $478632$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("j1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 478632j have rank \(0\).

Complex multiplication

The elliptic curves in class 478632j do not have complex multiplication.

Modular form 478632.2.a.j

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} + q^{11} + 2 q^{15} - 6 q^{19} + O(q^{20})\) 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 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 478632j

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
478632.j1 478632j1 \([0, -1, 0, -2890507419, -59813917940160]\) \(1418854149881269000523696128/21413352213\) \(40308151592115792\) \([2]\) \(161021952\) \(3.6667\) \(\Gamma_0(N)\)-optimal
478632.j2 478632j2 \([0, -1, 0, -2890504724, -59814035056236]\) \(-88678136326676754811067728/344501617579257699\) \(-10375749326485014791590656\) \([2]\) \(322043904\) \(4.0133\)