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Properties

Label 435600jx
Number of curves $6$
Conductor $435600$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jx1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 435600jx have rank \(1\).

Complex multiplication

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

Modular form 435600.2.a.jx

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 435600jx

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435600.jx5 435600jx1 \([0, 0, 0, -4773450, -6709404625]\) \(-37256083456/38671875\) \(-12485871965917968750000\) \([2]\) \(23592960\) \(2.9352\) \(\Gamma_0(N)\)-optimal*
435600.jx4 435600jx2 \([0, 0, 0, -89851575, -327709170250]\) \(15529488955216/6125625\) \(31644193910422500000000\) \([2, 2]\) \(47185920\) \(3.2818\) \(\Gamma_0(N)\)-optimal*
435600.jx3 435600jx3 \([0, 0, 0, -103464075, -221844757750]\) \(5927735656804/2401490025\) \(49623159122568147600000000\) \([2, 2]\) \(94371840\) \(3.6284\) \(\Gamma_0(N)\)-optimal*
435600.jx1 435600jx4 \([0, 0, 0, -1437489075, -20977558582750]\) \(15897679904620804/2475\) \(51142131572400000000\) \([2]\) \(94371840\) \(3.6284\)  
435600.jx2 435600jx5 \([0, 0, 0, -762309075, 7945856707250]\) \(1185450336504002/26043266205\) \(1076289411580726004640000000\) \([2]\) \(188743680\) \(3.9749\) \(\Gamma_0(N)\)-optimal*
435600.jx6 435600jx6 \([0, 0, 0, 337580925, -1614223822750]\) \(102949393183198/86815346805\) \(-3587815667721087649440000000\) \([2]\) \(188743680\) \(3.9749\)  
*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 435600jx1.