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Properties

Label 254800.cs
Number of curves $3$
Conductor $254800$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cs1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 254800.cs have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(5\)\(1\)
\(7\)\(1\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + T + 3 T^{2}\) 1.3.b
\(11\) \( 1 - 3 T + 11 T^{2}\) 1.11.ad
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 - 2 T + 19 T^{2}\) 1.19.ac
\(23\) \( 1 - 9 T + 23 T^{2}\) 1.23.aj
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 254800.cs do not have complex multiplication.

Modular form 254800.2.a.cs

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 254800.cs

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254800.cs1 254800cs3 \([0, -1, 0, -989862671408, -402005580473626688]\) \(-14245586655234650511684983641/1028175397808386133196800\) \(-7741683672112564491806100684800000000\) \([]\) \(5267275776\) \(5.8280\)  
254800.cs2 254800cs1 \([0, -1, 0, -11337571408, 503839174373312]\) \(-21405018343206000779641/2177246093750000000\) \(-16393652843750000000000000000000\) \([]\) \(585252864\) \(4.7294\) \(\Gamma_0(N)\)-optimal
254800.cs3 254800cs2 \([0, -1, 0, 69818678592, -462165200626688]\) \(4998853083179567995470359/2905108466204672000000\) \(-21874118780192861192192000000000000\) \([]\) \(1755758592\) \(5.2787\)