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Properties

Label 235200bbn
Number of curves $6$
Conductor $235200$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bbn1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 235200bbn have rank \(1\).

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
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 235200.2.a.bbn

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 235200bbn

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.bbn4 235200bbn1 \([0, 1, 0, -859133, -306788637]\) \(37256083456/525\) \(988251600000000\) \([2]\) \(2359296\) \(2.0174\) \(\Gamma_0(N)\)-optimal
235200.bbn3 235200bbn2 \([0, 1, 0, -883633, -288389137]\) \(2533446736/275625\) \(8301313440000000000\) \([2, 2]\) \(4718592\) \(2.3640\)  
235200.bbn2 235200bbn3 \([0, 1, 0, -3333633, 2031760863]\) \(34008619684/4862025\) \(585740676326400000000\) \([2, 2]\) \(9437184\) \(2.7106\)  
235200.bbn5 235200bbn4 \([0, 1, 0, 1174367, -1430579137]\) \(1486779836/8203125\) \(-988251600000000000000\) \([2]\) \(9437184\) \(2.7106\)  
235200.bbn1 235200bbn5 \([0, 1, 0, -51353633, 141625900863]\) \(62161150998242/1607445\) \(387306079856640000000\) \([2]\) \(18874368\) \(3.0572\)  
235200.bbn6 235200bbn6 \([0, 1, 0, 5486367, 10966420863]\) \(75798394558/259416045\) \(-62505038393763840000000\) \([2]\) \(18874368\) \(3.0572\)