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Properties

Label 436800.ov
Number of curves $2$
Conductor $436800$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ov1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 436800.2.a.ov

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + 6 q^{11} - q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 436800.ov

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.ov1 436800ov2 \([0, 1, 0, -19992833, 34234526463]\) \(1726143065560493/9662982966\) \(4947447278592000000000\) \([2]\) \(40550400\) \(3.0051\) \(\Gamma_0(N)\)-optimal*
436800.ov2 436800ov1 \([0, 1, 0, -552833, 1128206463]\) \(-36495256013/1053197964\) \(-539237357568000000000\) \([2]\) \(20275200\) \(2.6585\) \(\Gamma_0(N)\)-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.ov1.