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Properties

Label 436800.jy
Number of curves $2$
Conductor $436800$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jy1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436800.jy have rank \(1\).

Complex multiplication

The elliptic curves in class 436800.jy do not have complex multiplication.

Modular form 436800.2.a.jy

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 436800.jy

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.jy1 436800jy2 \([0, -1, 0, -5879193633, 173512059571137]\) \(-5486773802537974663600129/2635437714\) \(-10794752876544000000\) \([]\) \(221276160\) \(3.8910\) \(\Gamma_0(N)\)-optimal*
436800.jy2 436800jy1 \([0, -1, 0, 1142367, 5309539137]\) \(40251338884511/2997011332224\) \(-12275758416789504000000\) \([]\) \(31610880\) \(2.9180\) \(\Gamma_0(N)\)-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 436800.jy1.