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Properties

Label 435600.jr
Number of curves $6$
Conductor $435600$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jr1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 435600.jr have rank \(0\).

Complex multiplication

The elliptic curves in class 435600.jr do not have complex multiplication.

Modular form 435600.2.a.jr

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 435600.jr

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435600.jr1 435600jr5 \([0, 0, 0, -1692315075, 26794986237250]\) \(6484907238722641/283593750\) \(23440143637350000000000000\) \([2]\) \(141557760\) \(3.9462\) \(\Gamma_0(N)\)-optimal*
435600.jr2 435600jr4 \([0, 0, 0, -511839075, -4457026862750]\) \(179415687049201/1443420\) \(119304364532094720000000\) \([2]\) \(70778880\) \(3.5996\)  
435600.jr3 435600jr3 \([0, 0, 0, -111087075, 374247585250]\) \(1834216913521/329422500\) \(27228070849145760000000000\) \([2, 2]\) \(70778880\) \(3.5996\) \(\Gamma_0(N)\)-optimal*
435600.jr4 435600jr2 \([0, 0, 0, -32679075, -66483782750]\) \(46694890801/3920400\) \(324036545642726400000000\) \([2, 2]\) \(35389440\) \(3.2531\) \(\Gamma_0(N)\)-optimal*
435600.jr5 435600jr1 \([0, 0, 0, 2168925, -4767974750]\) \(13651919/126720\) \(-10473908546027520000000\) \([2]\) \(17694720\) \(2.9065\) \(\Gamma_0(N)\)-optimal*
435600.jr6 435600jr6 \([0, 0, 0, 215612925, 2160316485250]\) \(13411719834479/32153832150\) \(-2657641235348953814400000000\) \([2]\) \(141557760\) \(3.9462\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 435600.jr1.