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Properties

Label 436800rz
Number of curves $4$
Conductor $436800$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("rz1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436800rz have rank \(0\).

Complex multiplication

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

Modular form 436800.2.a.rz

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 436800rz

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.rz3 436800rz1 \([0, 1, 0, -11908, 474938]\) \(186756901696/8996715\) \(8996715000000\) \([2]\) \(983040\) \(1.2457\) \(\Gamma_0(N)\)-optimal
436800.rz2 436800rz2 \([0, 1, 0, -33033, -1700937]\) \(62287505344/16769025\) \(1073217600000000\) \([2, 2]\) \(1966080\) \(1.5922\)  
436800.rz4 436800rz3 \([0, 1, 0, 83967, -10943937]\) \(127871714872/175573125\) \(-89893440000000000\) \([2]\) \(3932160\) \(1.9388\)  
436800.rz1 436800rz4 \([0, 1, 0, -488033, -131375937]\) \(25107427013768/2985255\) \(1528450560000000\) \([2]\) \(3932160\) \(1.9388\)