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Properties

Label 283920.ce
Number of curves $4$
Conductor $283920$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ce1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 283920.ce have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 283920.ce do not have complex multiplication.

Modular form 283920.2.a.ce

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} - 4 q^{11} - q^{15} - 2 q^{17} + 8 q^{19} + O(q^{20})\) 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 283920.ce

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.ce1 283920ce3 \([0, -1, 0, -894888755440, 202545032310411712]\) \(4008766897254067912673785886329/1423480510711669921875000000\) \(28143077541591796875000000000000000000\) \([4]\) \(6936330240\) \(5.8869\)  
283920.ce2 283920ce2 \([0, -1, 0, -378272466160, -87240749481934400]\) \(302773487204995438715379645049/8911747415025000000000000\) \(176190679566620283801600000000000000\) \([2, 2]\) \(3468165120\) \(5.5404\)  
283920.ce3 283920ce1 \([0, -1, 0, -375558948080, -88585844735819328]\) \(296304326013275547793071733369/268420373544960000000\) \(5306834431222476114493440000000\) \([2]\) \(1734082560\) \(5.1938\) \(\Gamma_0(N)\)-optimal
283920.ce4 283920ce4 \([0, -1, 0, 94927533840, -290940478441934400]\) \(4784981304203817469820354951/1852343836482910078035000000\) \(-36621966954619857759641765130240000000\) \([2]\) \(6936330240\) \(5.8869\)