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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("u1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 436800.2.a.u

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 4 q^{11} - q^{13} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 436800.u

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.u1 436800u3 \([0, -1, 0, -529519973633, 92191680382015137]\) \(4008766897254067912673785886329/1423480510711669921875000000\) \(5830576171875000000000000000000000000\) \([2]\) \(7927234560\) \(5.7557\) \(\Gamma_0(N)\)-optimal*
436800.u2 436800u2 \([0, -1, 0, -223829861633, -39709017594304863]\) \(302773487204995438715379645049/8911747415025000000000000\) \(36502517411942400000000000000000000\) \([2, 2]\) \(3963617280\) \(5.4092\) \(\Gamma_0(N)\)-optimal*
436800.u3 436800u1 \([0, -1, 0, -222224229633, -40321259526592863]\) \(296304326013275547793071733369/268420373544960000000\) \(1099449850040156160000000000000\) \([2]\) \(1981808640\) \(5.0626\) \(\Gamma_0(N)\)-optimal*
436800.u4 436800u4 \([0, -1, 0, 56170138367, -132426257594304863]\) \(4784981304203817469820354951/1852343836482910078035000000\) \(-7587200354233999679631360000000000000\) \([2]\) \(7927234560\) \(5.7557\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 436800.u1.