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Properties

Label 235200.bbs
Number of curves $4$
Conductor $235200$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bbs1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 235200.bbs have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 235200.bbs do not have complex multiplication.

Modular form 235200.2.a.bbs

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 235200.bbs

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.bbs1 235200bbs4 \([0, 1, 0, -500094001633, -136121307995711137]\) \(229625675762164624948320008/9568125\) \(576348333120000000000\) \([2]\) \(990904320\) \(4.8842\)  
235200.bbs2 235200bbs2 \([0, 1, 0, -31255876633, -2126903032586137]\) \(448487713888272974160064/91549016015625\) \(689321611854225000000000000\) \([2, 2]\) \(495452160\) \(4.5377\)  
235200.bbs3 235200bbs3 \([0, 1, 0, -31148713633, -2142211374299137]\) \(-55486311952875723077768/801237030029296875\) \(-48263544497109375000000000000000\) \([2]\) \(990904320\) \(4.8842\)  
235200.bbs4 235200bbs1 \([0, 1, 0, -1960191508, -32993938276762]\) \(7079962908642659949376/100085966990454375\) \(11775013930459966764375000000\) \([2]\) \(247726080\) \(4.1911\) \(\Gamma_0(N)\)-optimal